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| 2. |
- Berglund, Erik, 1993-
(författare)
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Novel Hessian approximations in optimization algorithms
- 2022
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- There are several benefits of taking the Hessian of the objective function into account when designing optimization algorithms. Compared to using strictly gradient-based algorithms, Hessian-based algorithms usually require fewer iterations to converge. They are generally less sensitive to tuning of parameters and can better handle ill-conditioned problems. Yet, they are not universally used, due to there being several challenges associated with adapting them to various challenging settings. This thesis deals with Hessian-based optimization algorithms for large-scale, distributed and zeroth-order problems. For the large-scale setting, we contribute with a new way of deriving limited memory quasi-Newton methods, which we show can achieve better results than traditional limited memory quasi-Newton methods with less memory for some logistic and linear regression problems. For the distributed setting, we perform an analysis of how the error of a Newton-step is affected by the condition number and the number of iterations of a consensus-algorithm based on averaging, We show that the number of iterations needed to solve a quadratic problem with relative error less than ε grows logarithmically with 1/ε and also with the condition number of the Hessian of the centralized problem. For the zeroth order setting, we exploit the fact that a finite difference estimate of the directional derivative works as an approximate sketching technique, and use this to propose a zeroth order extension of a sketched Newton method that has been developed to solve large-scale problems. With the extension of this method to the zeroth order setting, we address the combined challenge of large-scale and zeroth order problems.
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| 3. |
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| 4. |
- Chaffey, Thomas, et al.
(författare)
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Circuit analysis using monotone+skew splitting
- 2023
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Ingår i: European Journal of Control. - 0947-3580.
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that the behavior of an m-port circuit of maximal monotone elements can be expressed as a zero of the sum of a maximal monotone operator containing the circuit elements, and a structured skew-symmetric linear operator representing the interconnection structure, together with a linear output transformation. The Condat–Vũ algorithm solves inclusion problems of this form, and may be used to solve for the periodic steady-state behavior, given a periodic excitation at each port, using an iteration in the space of periodic trajectories.
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| 5. |
- Chakraborty, Sucharita, et al.
(författare)
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Efficient downlink power allocation algorithms for cell-free massive mimo systems
- 2021
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Ingår i: IEEE Open Journal of the Communications Society. - : Institute of Electrical and Electronics Engineers (IEEE). - 2644-125X. ; 2, s. 168-186
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Tidskriftsartikel (refereegranskat)abstract
- Cell-free Massive MIMO systems consist of a large number of geographically distributed access points (APs) that serve the users by coherent joint transmission. The spectral efficiency (SE) achieved by each user depends on the power allocation: which APs that transmit to which users and with what power. In this article, we revisit the max-min and sum-SE power allocation policies, which have previously been approached using high-complexity general-purpose solvers. We develop and compare several different high-performance low-complexity power allocation algorithms that are appropriate for use in large systems. We propose two new algorithms for sum-SE power optimization inspired by weighted minimum mean square error (WMMSE) minimization and fractional programming (FP). Further, one new FP-based algorithm is proposed for max-min fair power allocation. The alternating direction method of multipliers (ADMM) is used to solve specific convex subproblems in the proposed algorithms. Our ADMM reformulations lead to multiple small-sized subproblems with closed-form solutions. The proposed algorithms find global or local optimal power allocation solutions for large-scale systems but with reduced computational time compared to previous work.
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| 6. |
- Darup, Moritz Schulze, et al.
(författare)
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Towards real-time ADMM for linear MPC
- 2019
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Ingår i: 2019 18th European Control Conference, ECC 2019. - 9783907144008 ; , s. 4276-4282
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Konferensbidrag (refereegranskat)abstract
- We present a novel predictive control scheme for linear constrained systems that uses the alternating direction method of multipliers (ADMM) for online optimization. In contrast to existing works on ADMM-based model predictive control (MPC), we only consider a single ADMM-iteration in every time step. The resulting real-time ADMM scheme is tailored for embedded and fast MPC implementations. The main difference to existing MPC schemes based on real-time iterations is that the proposed controller allows to include state and input constraints of the system. The paper derives the dynamics of the resulting closed-loop system, identifies important parameters of the real-time ADMM, and compares its performance to classical MPC.
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| 7. |
- Doan, Minh Dang, et al.
(författare)
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A distributed accelerated gradient algorithm for distributed model predictive control of a hydro power valley
- 2013
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Ingår i: Control Engineering Practice. - : Elsevier BV. - 0967-0661. ; 21:11, s. 1594-1605
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Tidskriftsartikel (refereegranskat)abstract
- A distributed model predictive control (DMPC) approach based on distributed optimization is applied to the power reference tracking problem of a hydro power valley (HPV) system. The applied optimization algorithm is based on accelerated gradient methods and achieves a convergence rate of O(1/k^2), where k is the iteration number. Major challenges in the control of the HPV include a nonlinear and large-scale model, non-smoothness in the power-production functions, and a globally coupled cost function that prevents distributed schemes to be applied directly. We propose a linearization and approximation approach that accommodates the proposed the DMPC framework and provides very similar performance compared to a centralized solution in simulations. The provided numerical studies also suggest that for the sparsely interconnected system at hand, the distributed algorithm we propose is faster than a centralized state-of-the-art solver such as CPLEX.
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| 8. |
- Fält, Mattias, et al.
(författare)
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Line Search for Generalized Alternating Projections
- 2016
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- This paper is about line search for the generalized alternating projections (GAP) method. This method is a generalization of the von Neumann alternating projections method, where instead of performing alternating projections, relaxed projections are alternated. The method can be interpreted as an averaged iteration of a nonexpansive mapping. Therefore, a recently proposed line search method for such algorithms is applicable to GAP. We evaluate this line search and show situations when the line search can be performed with little additional cost. We also present a variation of the basic line search for GAP - the projected line search. We prove its convergence and show that the line search condition is convex in the step length parameter. We show that almost all convex optimization problems can be solved using this approach and numerical results show superior performance with both the standard and the projected line search, sometimes by several orders of magnitude, compared to the nominal method.
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| 9. |
- Fält, Mattias, et al.
(författare)
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Line search for generalized alternating projections
- 2017
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Ingår i: 2017 American Control Conference, ACC 2017. - 9781509059928 ; , s. 4637-4642
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Konferensbidrag (refereegranskat)abstract
- This paper is about line search for the generalized alternating projections (GAP) method. This method is a generalization of the von Neumann alternating projections method, where instead of alternating projections, relaxed projections are alternated. The method can be interpreted as an averaged iteration of a nonexpansive mapping. Therefore, a recently proposed line search method for such algorithms is applicable to GAP. We evaluate this line search and show situations when the line search can be performed with little additional cost. We also present a variation of the basic line search for GAP - The projected line search. We prove its convergence and show that the line search condition is convex in the step length parameter. We show that almost all convex optimization problems can be solved using this approach and numerical results show superior performance with both the standard and the projected line search, sometimes by several orders of magnitude, compared to the nominal method.
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| 10. |
- Fält, Mattias, et al.
(författare)
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Optimal convergence rates for generalized alternating projections
- 2017
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Ingår i: Proceedings of the IEEE Conference on Decision and Control, 2017. - 9781509028740 - 9781509028733 ; , s. 2268-2274
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Konferensbidrag (refereegranskat)abstract
- Generalized alternating projections is an algorithm that alternates relaxed projections onto a finite number of sets to find a point in their intersection. We consider the special case of two linear subspaces, for which the algorithm reduces to matrix multiplications. For convergent powers of the matrix, the asymptotic rate is linear and decided by the magnitude of the subdominant eigenvalue. In this paper, we show how to select the three algorithm parameters to optimize this magnitude, and hence the asymptotic convergence rate. The obtained rate depends on the Friedrichs angle between the subspaces and is considerably better than known rates for other methods such as alternating projections and DouglasRachford splitting. We also present an adaptive scheme that, online, estimates the Friedrichs angle and updates the algorithm parameters based on this estimate. A numerical example is provided that supports our theoretical claims and shows very good performance for the adaptive method.
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