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1.	Assran, By Mahmoud, et al. (författare) Advances in Asynchronous Parallel and Distributed Optimization 2020 Ingår i: Proceedings of the IEEE. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9219 .- 1558-2256. ; 108:11, s. 2013-2031 Tidskriftsartikel (refereegranskat)abstract Motivated by large-scale optimization problems arising in the context of machine learning, there have been several advances in the study of asynchronous parallel and distributed optimization methods during the past decade. Asynchronous methods do not require all processors to maintain a consistent view of the optimization variables. Consequently, they generally can make more efficient use of computational resources than synchronous methods, and they are not sensitive to issues like stragglers (i.e., slow nodes) and unreliable communication links. Mathematical modeling of asynchronous methods involves proper accounting of information delays, which makes their analysis challenging. This article reviews recent developments in the design and analysis of asynchronous optimization methods, covering both centralized methods, where all processors update a master copy of the optimization variables, and decentralized methods, where each processor maintains a local copy of the variables. The analysis provides insights into how the degree of asynchrony impacts convergence rates, especially in stochastic optimization methods.
2.	Aytekin, Arda, 1986-, et al. (författare) Asynchronous incremental block-coordinate descent 2014 Ingår i: 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton). - : IEEE conference proceedings. ; , s. 19-24 Konferensbidrag (refereegranskat)abstract This paper studies a flexible algorithm for minimizing a sum of component functions, each of which depends on a large number of decision variables. Such formulations appear naturally in “big data” applications, where each function describes the loss estimated using the data available at a specific machine, and the number of features under consideration is huge. In our algorithm, a coordinator updates a global iterate based on delayed partial gradients of the individual objective functions with respect to blocks of coordinates. Delayed incremental gradient and delayed coordinate descent algorithms are obtained as special cases. Under the assumption of strong convexity and block coordinate-wise Lipschitz continuous partial gradients, we show that the algorithm converges linearly to a ball around the optimal value. Contrary to related proposals in the literature, our algorithm is delay-insensitive: it converges for any bounded information delay, and its step-size parameter can be chosen independently of the maximum delay bound.
3.	Besselink, B., et al. (författare) D-stability and delay-independent stability of monotone nonlinear systems with max-separable Lyapunov functions 2016 Ingår i: 2016 IEEE 55th Conference on Decision and Control, CDC 2016. - : Institute of Electrical and Electronics Engineers (IEEE). - 9781509018376 ; , s. 3172-3177 Konferensbidrag (refereegranskat)abstract Stability properties of monotone nonlinear systems with max-separable Lyapunov functions are considered in this paper, motivated by the following observations. First, recent results have shown that such Lyapunov functions are guaranteed to exist for asymptotically stable monotone systems on compact sets. Second, it is well-known that, for monotone linear systems, asymptotic stability implies the stronger properties of D-stability and robustness with respect to time-delays. This paper shows that similar properties hold for monotone nonlinear systems that admit max-separable Lyapunov functions. In particular, a notion of D-stability for monotone nonlinear systems and delay-independent stability will be discussed. The theoretical results are illustrated by means of examples.
4.	Demirel, Burak, et al. (författare) Stability Analysis of Discrete-Time Linear Systems with Unbounded Stochastic Delays 2015 Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. Konferensbidrag (refereegranskat)abstract This paper investigates the stability of discrete-time linear systems with stochastic delays. We assume that delays are modeled as random variables, which take values in integers with a certain probability. For the scalar case, we provide an analytical bound on the probability to guarantee the stability of linear systems. In the vector case, we derive a linear matrix inequality condition to compute the probability for ensuring the stability of closed-loop systems. As a special case, we also determine the step size of gradient algorithms with stochastic delays in the unconstrained quadratic programming to guarantee convergence to the optimal solution. Numerical examples are provided to show the effectiveness of the proposed analysis techniques.
5.	do Nascimento, Allan Andre, et al. (författare) Tube-based Model Predictive Control for Dynamic Positioning of Marine Vessels 2019 Ingår i: IFAC PAPERSONLINE. - : ELSEVIER. - 2405-8963. ; , s. 33-38 Konferensbidrag (refereegranskat)abstract This paper focuses on the design of a robust model predictive control law for dynamic positioning (DP) of marine vessels in the presence of actuator saturation and environmental disturbances. The proposed solution is a tube-based MPC ensuring robustness and constraint fulfillment. Formulation of the tube-based MPC relies on a sufficient robust invariant set condition, along with a linear matrix inequality (LMI) synthesis procedure, and an efficient analytical Pontryagin set difference computation. Simulation results show the effectiveness and satisfactory behaviour of the proposed controller.
6.	Feyzmahdavian, Hamid Reza, et al. (författare) A delayed proximal gradient method with linear convergence rate 2014 Ingår i: IEEE International Workshop on Machine Learning for Signal Processing (MLSP). - : IEEE conference proceedings. ; , s. 1-6 Konferensbidrag (refereegranskat)abstract This paper presents a new incremental gradient algorithm for minimizing the average of a large number of smooth component functions based on delayed partial gradients. Even with a constant step size, which can be chosen independently of the maximum delay bound and the number of objective function components, the expected objective value is guaranteed to converge linearly to within some ball around the optimum. We derive an explicit expression that quantifies how the convergence rate depends on objective function properties and algorithm parameters such as step-size and the maximum delay. An associated upper bound on the asymptotic error reveals the trade-off between convergence speed and residual error. Numerical examples confirm the validity of our results.
7.	Feyzmahdavian, Hamid Reza, et al. (författare) An Asynchronous Mini-Batch Algorithm for Regularized Stochastic Optimization 2015 Ingår i: 2015 54th IEEE Conference on Decision and Control (CDC). - : IEEE. - 9781479978847 ; , s. 1384-1389 Konferensbidrag (refereegranskat)abstract Mini-batch optimization has proven to be a powerful paradigm for large-scale learning. However, the state of the art mini-batch algorithms assume synchronous operation or cyclic update orders. When worker nodes are heterogeneous (due to different computational capabilities, or different communication delays), synchronous and cyclic operations are inefficient since they will leave workers idle waiting for the slower nodes to complete their work. We propose an asynchronous mini-batch algorithm for regularized stochastic optimization problems that eliminates idle waiting and allows workers to run at their maximal update rates. We show that the time necessary to compute an ϵ-optimal solution is asymptotically O(1/ϵ2), and the algorithm enjoys near-linear speedup if the number of workers is O(1/√ϵ). Theoretical results are confirmed in real implementations on a distributed computing infrastructure.
8.	Feyzmahdavian, Hamid Reza, et al. (författare) Asymptotic and Exponential Stability of General Classes of Continuous-Time Power Control Laws in Wireless Networks 2013 Ingår i: Proceedings of 52nd IEEE Conference on Decision and Control December 10-13, 2013. Florence, Italy. - : IEEE conference proceedings. ; , s. 49-54 Konferensbidrag (refereegranskat)abstract This paper develops a comprehensive stabilityanalysis framework for continuous-time power control algorithmsin wireless networks under bounded time-varyingcommunication delays. Our first set of results establish globalasymptotic stability of power control laws involving two-sidedscalable interference functions, and include earlier work onstandard interference functions as a special case. We thenconsider contractive interference functions and demonstratethat the associated continuous-time power control laws alwayshave unique fixed points, which are exponentially stable evenin the presence of bounded heterogeneous time-varying delays.For this class of interference functions, we derive an explicitbound on the decay rate that allows us to quantify the impactof delays on the convergence time of the algorithm. Numericalsimulations illustrate our theoretical results.
9.	Feyzmahdavian, Hamid Reza, et al. (författare) ASYMPTOTIC STABILITY AND DECAY RATES OF HOMOGENEOUS POSITIVE SYSTEMS WITH BOUNDED AND UNBOUNDED DELAYS 2014 Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 52:4, s. 2623-2650 Tidskriftsartikel (refereegranskat)abstract There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and establishes asymptotic stability and bounds the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Specifically, we present a necessary and sufficient condition for delay-independent stability of continuous-time positive systems whose vector fields are cooperative and homogeneous. We show that global asymptotic stability of such systems is independent of the magnitude and variation of the time delays. For various classes of time delays, we are able to derive explicit expressions that quantify the decay rates of positive systems. We also provide the corresponding counterparts for discrete-time positive systems whose vector fields are nondecreasing and homogeneous.
10.	Feyzmahdavian, Hamid Reza, et al. (författare) Asymptotic Stability and Decay Rates of Positive Linear Systems with Unbounded Delays 2013 Ingår i: Proceedings of the 52nd IEEE Conference on Decision and Control (CDC). - : IEEE conference proceedings. ; , s. 1423-1428 Konferensbidrag (refereegranskat)abstract There are several results on the stability analysisof positive linear systems in the presence of constant or timevaryingdelays. However, most existing results assume thatthe delays are bounded. This paper studies the stability ofdiscrete-time positive linear systems with unbounded delays.We provide a set of easily verifiable necessary and sufficientconditions for delay-independent stability of positive linearsystems subject to a general class of heterogeneous timevaryingdelays. For two particular classes of unbounded delays,explicit expressions that bound the decay rate of the system arepresented. We demonstrate that the best bound on the decayrate that our results can guarantee can be found via convexoptimization. Finally, the validity of the results is demonstratedvia a numerical example.
11.	Feyzmahdavian, Hamid Reza, et al. (författare) Asynchronous Iterations in Optimization : New Sequence Results and Sharper Algorithmic Guarantees 2023 Ingår i: Journal of machine learning research. - : MICROTOME PUBL. - 1532-4435 .- 1533-7928. ; 24 Tidskriftsartikel (refereegranskat)abstract We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony impacts the convergence rates of the iterates. Our results shorten, streamline and strengthen existing convergence proofs for several asynchronous optimization methods and allow us to establish convergence guarantees for popular algorithms that were thus far lacking a complete theoretical under-standing. Specifically, we use our results to derive better iteration complexity bounds for proximal incremental aggregated gradient methods, to obtain tighter guarantees depending on the average rather than maximum delay for the asynchronous stochastic gradient descent method, to provide less conservative analyses of the speedup conditions for asynchronous block-co ordinate implementations of Krasnosel'skii-Mann iterations, and to quantify the convergence rates for totally asynchronous iterations under various assumptions on communication delays and update rates.
12.	Feyzmahdavian, Hamid Reza, et al. (författare) Asynchronous Mini-Batch Algorithm for Regularized Stochastic Optimization 2016 Ingår i: IEEE Transactions on Automatic Control. - : IEEE. - 0018-9286 .- 1558-2523. Tidskriftsartikel (refereegranskat)abstract Mini-batch optimization has proven to be a powerful paradigm for large-scale learning. However, the state of the art parallel mini–batch algorithms assume synchronous operation or cyclic update orders. When worker nodes are heterogeneous (due to different computational capabilities or different communication delays), synchronous and cyclic operations are inefficient since they will leave workers idle waiting for the slower nodes to complete their computations. In this paper, we propose an asynchronous mini-batch algorithm for regularized stochastic optimization problems with smooth loss functions that eliminates idle waiting and allows workers to run at their maximal update rates. We show that by suitably choosing the step-size values, the algorithm achieves a rate of the order O(1/ √ T) for general convex regularization functions, and the rate O(1/T ) for strongly convex regularization functions, where T is the number of iterations. In both cases, the impact of asynchrony on the convergence rate of our algorithm is asymptotically negligible, and a nearlinear speedup in the number of workers can be expected. Theoretical results are confirmed in real implementations on a distributed computing infrastructure.
13.	Feyzmahdavian, Hamid Reza, et al. (författare) Contractive interference functions and rates of convergence of distributed power control laws 2012 Ingår i: IEEE International Conference on Communications (ICC), Ottawa, Canada.. - : IEEE. - 9781457720512 ; , s. 4395-4399 Konferensbidrag (refereegranskat)abstract The standard interference functions introduced by Yates have been very influential on the analysis and design of distributed power control laws. While powerful and versatile, the framework has some drawbacks: the existence of fixed-points has to be established separately, and no guarantees are given on the rate of convergence of the iterates. This paper introduces contractive interference functions, a slight reformulation of the standard interference functions that guarantees existence and uniqueness of fixed-points and geometric convergence rates. We show that many power control laws from the literature are contractive and derive, sometimes for the first time, convergence rate estimates for these algorithms. Finally, we show that although standard interference functions are not contractive, they are paracontractions with respect to a certain metric space. Extensions to two-sided scalable interference functions are also discussed.
14.	Feyzmahdavian, Hamid Reza, et al. (författare) Contractive interference functions and rates of convergence of distributed power control laws 2012 Ingår i: IEEE Transactions on Wireless Communications. - : IEEE Communications Society. - 1536-1276 .- 1558-2248. ; 11:12, s. 4494-4502 Tidskriftsartikel (refereegranskat)abstract The standard interference functions introduced by Yates have been very influential on the analysis and design of distributed power control laws. While powerful and versatile, the framework has some drawbacks: the existence of fixed-points has to be established separately, and no guarantees are given on the rate of convergence of the iterates. This paper introduces contractive interference functions, a slight reformulation of the standard interference functions that guarantees the existence and uniqueness of fixed-points along with linear convergence of iterates. We show that many power control laws from the literature are contractive and derive, sometimes for the first time, analytical convergence rate estimates for these algorithms. We also prove that contractive interference functions converge when executed totally asynchronously and, under the assumption that the communication delay is bounded, derive an explicit bound on the convergence time penalty due to increased delay. Finally, we demonstrate that although standard interference functions are, in general, not contractive, they are all para-contractions with respect to a certain metric. Similar results for two-sided scalable interference functions are also derived.
15.	Feyzmahdavian, Hamid Reza, et al. (författare) Delay-independent stability of cone-invariant monotone systems 2016 Ingår i: Proceedings of the IEEE Conference on Decision and Control. - : IEEE. - 0743-1546 .- 2576-2370. - 9781479978861 ; 2016-February, s. 6361-6366, s. 6361-6366 Konferensbidrag (refereegranskat)abstract Recent results in the literature have shown that particular classes of positive systems are insensitive to time-varying delays, giving the impression that the delay-insensitivity property stems from the fact that the system is positive. Nonetheless, it has been lately shown that a linear cone-invariant system is insensitive to time-varying delays, asserting that the property of delay-independence may stem from the fact that the system is cone-invariant rather than positive. In this paper, we provide additional evidence for this claim by analyzing the stability of cone-invariant monotone systems with bounded time-varying delays. We present a set of sufficient conditions for delay independent stability of discrete- and continuous-time cone-invariant monotone systems. For linear cone-invariant systems, we show that the stability conditions we have derived are also necessary.
16.	Feyzmahdavian, Hamid Reza, et al. (författare) Distributed Output-Feedback LQG Control with Delayed Information Sharing 2012 Ingår i: Estimation and Control of Networked Systems, Volume 3, Part 1. Konferensbidrag (refereegranskat)abstract This paper develops a controller synthesis method for distributed LQG controlproblems under output-feedback. We consider a system consisting of three interconnected linearsubsystems with a delayed information sharing structure. While the state-feedback case haspreviously been solved, the extension to output-feedback is nontrivial as the classical separationprinciple fails. To nd the optimal solution, the controller is decomposed into two independentcomponents: a centralized LQG-optimal controller under delayed state observations, and a sumof correction terms based on additional local information available to decision makers. Explicitdiscrete-time equations are derived whose solutions are the gains of the optimal controller.
17.	Feyzmahdavian, Hamid Reza, et al. (författare) Exponential Stability of Homogeneous Positive Systems of Degree One With Time-Varying Delays 2014 Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 59:6, s. 1594-1599 Tidskriftsartikel (refereegranskat)abstract While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of conditions for establishing delay-independent stability and bounding the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Specifically, when the time delays have a known upper bound, we derive necessary and sufficient conditions for exponential stability of (a) continuous-time positive systems whose vector fields are homogeneous and cooperative, and (b) discrete-time positive systems whose vector fields are homogeneous and order-preserving. We then present explicit expressions that allow us to quantify the impact of delays on the decay rate and show that the best decay rate of positive linear systems that our bounds provide can be found via convex optimization. Finally, we extend the results to general linear systems with time-varying delays.
18.	Feyzmahdavian, Hamid Reza, et al. (författare) On the Convergence Rates of Asynchronous Iterations 2014 Ingår i: Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on. - : IEEE conference proceedings. - 9781479977468 ; , s. 153-159 Konferensbidrag (refereegranskat)abstract This paper presents a unifying convergence result for asynchronous iterations involving pseudo-contractions in the block-maximum norm. Contrary to previous results which only established asymptotic convergence or studied simplified models of asynchronism, our result allows to bound the convergence rates for both partially and totally asynchronous implementations. Several examples are worked out to demonstrate that our theorem recovers and improves on existing results, and that it allows to characterize the solution times for several classes of asynchronous iterations that have not been addressed before.
19.	Feyzmahdavian, Hamid Reza, et al. (författare) On the rate of convergence of continuous-time linear positive systems with heterogeneous time-varying delays 2013 Ingår i: 2013 European Control Conference, ECC 2013. - : IEEE conference proceedings. - 9783033039629 ; , s. 3372-3377 Konferensbidrag (refereegranskat)abstract In this work, a set of conditions are presented for establishing exponential stability and bounds on the convergence rates of both general and positive linear systems with heterogeneous time-varying delays. First, a sufficient condition for delay-independent exponential stability of general linear systems is derived. When the time delays have a known upper bound, we present an explicit expression that bounds the decay rate of the system. We demonstrate that the best decay rate that our bound can guarantee can be easily found via convex optimization techniques. Finally, for positive linear systems, we show that the stability condition that we have developed is also necessary. The validity of the results is demonstrated via numerical examples.
20.	Feyzmahdavian, Hamid Reza, et al. (författare) Optimal Distributed Controller Design with Communication Delays : Application to vehicle formations 2012 Ingår i: 2012 IEEE 51st Annual Conference on Decision and Control (CDC). - : IEEE conference proceedings. - 9781467320665 ; , s. 2232-2237 Konferensbidrag (refereegranskat)abstract We consider the problem of optimal distributed control with delayed information sharing over chain structures motivated by applications of heavy duty vehicle platooning. We introduce a novel approach to find distributed controllers that take into account communication delays and correlation between the dynamic interconnection. The design decomposes the solution into separate optimization problems. The results show that a tight control is achieved, even in the presence of delays, and behaves well with respect to the imposed disturbances. The computed theoretical cost of the proposed optimal controller is significantly better than the theoretical cost for the centralized control with a global delay and close to the cost for a fully centralized control with full state information at all times.
21.	Feyzmahdavian, Hamid Reza (författare) Performance Analysis of Positive Systems and Optimization Algorithms with Time-delays 2016 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract Time-delay dynamical systems are used to model many real-world engineering systems, where the future evolution of a system depends not only on current states but also on the history of states. For this reason, the study of stability and control of time-delay systems is of theoretical and practical importance. In this thesis, we develop several stability analysis frameworks for dynamical systems in the presence of communication and computation time-delays, and apply our results to different challenging engineering problems.The thesis first considers delay-independent stability of positive monotone systems. We show that the asymptotic stability of positive monotone systems whose vector fields are homogeneous is independent of the magnitude and variation of time-varying delays. We present explicit expressions that allow us to give explicit estimates of the decay rate for various classes of time-varying delays. For positive linear systems, we demonstrate that the best decay rate that our results guarantee can be found via convex optimization. We also derive a set of necessary and sufficient conditions for asymptotic stability of general positive monotone (not necessarily homogeneous) systems with time-delays. As an application of our theoretical results, we discuss delay-independent stability of continuous-time power control algorithms in wireless networks.The thesis continues by studying the convergence of asynchronous fixed-point iterations involving maximum norm pseudo-contractions. We present a powerful approach for characterizing the rate of convergence of totally asynchronous iterations, where both the update intervals and communication delays may grow unbounded. When specialized to partially asynchronous iterations (where the update intervals and communication delays have a fixed upper bound), or to particular classes of unbounded delays and update intervals, our approach allows to quantify how the degree of asynchronism affects the convergence rate. In addition, we use our results to analyze the impact of asynchrony on the convergence rate of discrete-time power control algorithms in wireless networks.The thesis finally proposes an asynchronous parallel algorithm that exploits multiple processors to solve regularized stochastic optimization problems with smooth loss functions. The algorithm allows the processors to work at different rates, perform computations independently of each other, and update global decision variables using out-of-date gradients. We characterize the iteration complexity and the convergence rate of the proposed algorithm, and show that these compare favourably with the state of the art. Furthermore, we demonstrate that the impact of asynchrony on the convergence rate of the algorithm is asymptotically negligible, and a near-linear speedup in the number of processors can be expected.
22.	Feyzmahdavian, Hamid Reza, et al. (författare) Stability Analysis of Monotone Systems via Max-Separable Lyapunov Functions 2018 Ingår i: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 63:3, s. 643-656 Tidskriftsartikel (refereegranskat)abstract We analyze stability properties of monotone nonlinear systems via max-separable Lyapunov functions, motivated by the following observations: first, recent results have shown that asymptotic stability of a monotone nonlinear system implies the existence of a max-separable Lyapunov function on a compact set; second, for monotone linear systems, asymptotic stability implies the stronger properties of D-stability and insensitivity to time delays. This paper establishes that for monotone nonlinear systems, equivalence holds between asymptotic stability, the existence of a max-separable Lyapunov function, D-stability, and insensitivity to bounded and unbounded time-varying delays. In particular, a new and general notion of D-stability for monotone nonlinear systems is discussed, and a set of necessary and sufficient conditions for delay-independent stability are derived. Examples show how the results extend the state of the art.
23.	Feyzmahdavian, Hamid Reza, et al. (författare) Stability and Performance of Continuous-Time Power Control in Wireless Networks 2014 Ingår i: IEEE Transactions on Automatic Control. - : IEEE Robotics and Automation Society. - 0018-9286 .- 1558-2523. ; 59:8, s. 2012-2023 Tidskriftsartikel (refereegranskat)abstract This paper develops a comprehensive stability analysis framework for general classes of continuous-time power control algorithms under heterogeneous time-varying delays. Our first set of results establish global asymptotic stability of power control laws involving two-sided scalable interference functions, and include earlier work on standard interference functions as a special case. We then consider contractive interference functions and demonstrate that the associated continuous-time power control laws always have unique fixed points which are exponentially stable, even under bounded heterogeneous time-varying delays. For this class of interference functions, we present explicit bounds on the decay rate that allow us to quantify the impact of delays on the convergence time of the algorithm. When interference functions are linear, we also prove that contractivity is necessary and sufficient for exponential stability of continuous-time power control algorithms with time-varying delays. Finally, numerical simulations illustrate the validity of our theoretical results.
24.	Feyzmahdavian, Hamid Reza, et al. (författare) Sub-homogeneous positive monotone systems are insensitive to heterogeneous time-varying delays 2014 Ingår i: 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). Konferensbidrag (refereegranskat)abstract We show that a sub-homogeneous positive monotone system with bounded heterogeneous time-varying delays is globally asymptotically stable if and only if the corresponding delay-free system is globally asymptotically stable. The proof is based on an extension of a delay-independent stability result for monotone systems under constant delays by Smith to systems with bounded heterogenous time-varying delays. Under the additional assumption of positivity and sub-homogenousvector fields, we establish the aforementioned delay insensitivity property and derive a novel test for global asymptotic stability. If the system has a unique equilibrium point in the positive orthant, we prove that our stability test is necessary and sufficient. Specialized to positive linear systems, our results extend and sharpen existing results from the literature.
25.	Ghadimi, Euhanna, et al. (författare) Global Convergence of the Heavy-ball Method for Convex Optimization 2015 Ingår i: European Control Conference (ECC15). - : IEEE. Konferensbidrag (refereegranskat)abstract This paper establishes global convergence and provides global bounds of the rate of convergence for the Heavy-ball method for convex optimization. When the objective function has Lipschitz-continuous gradient, we show that the Cesáro average of the iterates converges to the optimum at a rate of O(1/k) where k is the number of iterations. When the objective function is also strongly convex, we prove that the Heavy-ball iterates converge linearly to the unique optimum. Numerical examples validate our theoretical findings.
26.	Halilovic, Amar, et al. (författare) Multi-constrained Network Occupancy Optimization 2021 Ingår i: ACM International Conference Proceeding Series. - New York, NY, USA : Association for Computing Machinery. - 9781450390576 Konferensbidrag (refereegranskat)abstract The greater the number of devices on a network, the higher load in the network, the more chance of a collision occurring, and the longer it takes to transmit a message. The size of load can be identified by measuring the network occupancy, hence it is desirable to minimize the latter. In this paper, we present an approach for network occupancy minimization by optimizing the packing process while satisfying multiple constraints. We formulate the minimization problem as a bin packing problem and we implement a modification of the Best-Fit Decreasing algorithm to find the optimal solution. The approach considers grouping signals that are sent to different destinations in the same package. The analysis is done on a medium-sized plant model, and different topologies are tested. The results show that the proposed solution lowers the network occupancy compared to a reference case.
27.	Khirirat, Sarit, et al. (författare) Mini-batch gradient descent : faster convergence under data sparsity 2017 Ingår i: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781509028733 Konferensbidrag (refereegranskat)abstract The practical performance of stochastic gradient descent on large-scale machine learning tasks is often much better than what current theoretical tools can guarantee. This indicates that there is an inherent structure in these problems that could be exploited to strengthen the analysis. In this paper, we argue that data sparsity is such a property. We derive explicit expressions for how data sparsity affects the range of admissible step-sizes and the convergence factors of mini-batch gradient descent. Our theoretical results are validated by solving least-squares support vector machine problems on both synthetic and real-life data sets. The experimental results demonstrate improved performance of our update rules compared to the traditional mini-batch gradient descent algorithm.
28.	Lu, Jie, et al. (författare) Dual coordinate descent algorithms for multi-agent optimization 2015 Ingår i: European Control Conference (ECC15). - : IEEE conference proceedings. Konferensbidrag (refereegranskat)abstract Multi-agent optimization problems arise in a wide variety of networked systems, and are often required to be solved in an asynchronous and uncoordinated way. However, existing asynchronous algorithms for constrained multi-agent optimization do not have guaranteed convergence rates and, thus, lack performance guarantees in on-line applications. This paper addresses this shortcoming by developing randomized coordinate descent algorithms for solving the dual of a class of constrained multi-agent optimization problems. We show that the algorithms can be implemented asynchronously and distributively in multi-agent networks. Moreover, without relying on the standard assumption of boundedness of the dual optimal set, the proposed dual coordinate descent algorithms achieve sublinear convergence rates of both its primal and dual iterates in expectation. The competitive performance is demonstrated numerically on a constrained optimal rendezvous problem.
29.	Qazizadeh, Alireza, et al. (författare) Wheelset curving guidance using H∞ control 2018 Ingår i: Vehicle System Dynamics. - : Taylor & Francis. - 0042-3114 .- 1744-5159. ; 56:3, s. 461-484 Tidskriftsartikel (refereegranskat)abstract This study shows how to design an active suspension system for guidance of a rail vehicle wheelset in curve. The main focus of the study is on designing the controller and afterwards studying its effect on the wheel wear behaviour. The controller is designed based on the closed-loop transfer function shaping method and (Formula presented.) control strategy. The study discusses designing of the controller for both nominal and uncertain plants and considers both stability and performance. The designed controllers in Simulink are then applied to the vehicle model in Simpack to study the wheel wear behaviour in curve. The vehicle type selected for this study is a two-axle rail vehicle. This is because this type of vehicle is known to have very poor curving performance and high wheel wear. On the other hand, the relative simpler structure of this type of vehicle compared to bogie vehicles make it a more economic choice. Hence, equipping this type of vehicle with the active wheelset steering is believed to show high enough benefit to cost ratio to remain attractive to rail vehicle manufacturers and operators.
30.	Qazizadeh, Alireza, et al. (författare) Wheelset Curving Guidance Using H_infinity Control Ingår i: Vehicle System Dynamics. - 0042-3114 .- 1744-5159. Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract This study shows how to design an active suspension system for guidance of a rail vehiclewheelset in curve. The main focus of the study is on designing the controller and afterwardsstudying its eect on the wheel wear behavior. The controller is designed based on theclosed-loop transfer function shaping method and H1 control strategy. The study discussesdesigning of the controller for both nominal and uncertain plants and considers both stabilityand performance. The designed controllers in Simulink are then applied to the vehicle modelin Simpack to study the wheel wear behavior in curve. The vehicle type selected for thisstudy is a two-axle rail vehicle. This is because this type of vehicle is known to have verypoor curving performance and high wheel wear. On the other hand, the relative simplerstructure of this type of vehicle compared to bogie vehicles make it a more economic choice.Hence, equipping this type of vehicle with the active wheelset steering is believed to show highenough benet to cost ratio to remain attractive to rail vehicle manufacturers and operators.
31.	Wu, Xuyang, et al. (författare) Delay-adaptive step-sizes for asynchronous learning 2022 Ingår i: Proceedings of the 39th International Conference on Machine Learning. - : ML Research Press. ; , s. 24093-24113 Konferensbidrag (refereegranskat)abstract In scalable machine learning systems, model training is often parallelized over multiple nodes that run without tight synchronization. Most analysis results for the related asynchronous algorithms use an upper bound on the information delays in the system to determine learning rates. Not only are such bounds hard to obtain in advance, but they also result in unnecessarily slow convergence. In this paper, we show that it is possible to use learning rates that depend on the actual time-varying delays in the system. We develop general convergence results for delay-adaptive asynchronous iterations and specialize these to proximal incremental gradient descent and block coordinate descent algorithms. For each of these methods, we demonstrate how delays can be measured on-line, present delay-adaptive step-size policies, and illustrate their theoretical and practical advantages over the state-of-the-art.
32.	Wu, Xuyang, et al. (författare) Optimal convergence rates of totally asynchronous optimization 2022 Ingår i: 2022 IEEE 61st Conference on Decision and Control (CDC), Cancun, Mexico, 2022. - : IEEE (Institute of Electrical and Electronics Engineers). - 9781665467612 ; , s. 6484-6490 Konferensbidrag (refereegranskat)abstract Asynchronous optimization algorithms are at the core of modern machine learning and resource allocation systems. However, most convergence results consider bounded information delays and several important algorithms lack guarantees when they operate under total asynchrony. In this paper, we derive explicit convergence rates for the proximal incremental aggregated gradient (PIAG) and the asynchronous block-coordinate descent (Async-BCD) methods under a specific model of total asynchrony, and show that the derived rates are order-optimal. The convergence bounds provide an insightful understanding of how the growth rate of the delays deteriorates the convergence times of the algorithms. Our theoretical findings are demonstrated by a numerical example.
33.	Åstrand, Max, et al. (författare) Short-Term Scheduling of Production Fleets in Underground Mines Using CP-Based LNS 2021 Ingår i: Lecture Notes in Computer Science. - Cham : Springer Nature. ; , s. 365-382 Konferensbidrag (refereegranskat)abstract Coordinating the mobile production fleet in underground mines becomes increasingly important as the machines are more and more automated. We present a scheduling approach that applies to several of the most important production methods used in underground mines. Our algorithm combines constraint programming with a large neighborhood search strategy that dynamically adjusts the neighborhood size. The resulting algorithm is complete and able to rapidly improve constructed schedules in practice. In addition, it has important benefits when it comes to the acceptance of the approach in real-life operations. Our approach is evaluated on public and private industrial problem instances representing different mines and production methods. We find significant improvements over the current industrial practice.

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