| 1. |
- Egidio, Lucas N., et al.
(author)
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Learning the Step-size Policy for the Limited-Memory Broyden-Fletcher-Goldfarb-Shanno Algorithm
- 2021
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In: 2021 international joint conference on neural networks (IJCNN). - : Institute of Electrical and Electronics Engineers (IEEE). - 9780738133669
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Conference paper (peer-reviewed)abstract
- We consider the problem to learn a step-size policy for the Limited-Memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. This is a limited computational memory quasi-Newton method widely used for deterministic unconstrained optimization. However, L-BFGS is currently avoided in large-scale problems for requiring step sizes to be provided at each iteration. Current methodologies for the step size selection for L-BFGS use heuristic tuning of design parameters and massive re-evaluations of the objective function and gradient to find appropriate step-lengths. We propose a neural network architecture with local information of the current iterate as the input. The step-length policy is learned from data of similar optimization problems, avoids additional evaluations of the objective function, and guarantees that the output step remains inside a pre-defined interval. The corresponding training procedure is formulated as a stochastic optimization problem using the backpropagation through time algorithm. The performance of the proposed method is evaluated on the training of image classifiers for the MNIST database for handwritten digits and for CIFAR-10. The results show that the proposed algorithm outperforms heuristically tuned optimizers such as ADAM, RMSprop, L-BFGS with a backtracking line search, and L-BFGS with a constant step size. The numerical results also show that a learned policy can be used as a warm-start to train new policies for different problems after a few additional training steps, highlighting its potential use in multiple large-scale optimization problems.
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| 2. |
- Ahmadi, Shervin Parvini, et al.
(author)
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A Distributed Second-Order Augmented Lagrangian Method for Distributed Model Predictive Control
- 2021
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In: IFAC PAPERSONLINE. - : ELSEVIER. - 2405-8963. ; , s. 192-199
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Conference paper (peer-reviewed)abstract
- In this paper we present a distributed second-order augmented Lagrangian method for distributed model predictive control. We distribute the computations for search direction, step size, and termination criteria over what is known as the clique tree of the problem and calculate each of them using message passing. The algorithm converges to its centralized counterpart and it requires fewer communications between sub-systems as compared to algorithms such as the alternating direction method of multipliers. Results from a simulation study confirm the efficiency of the framework. Copyright (C) 2021 The Authors.
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| 3. |
- Ahmadi, Shervin Parvini, et al.
(author)
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Efficient Robust Model Predictive Control using Chordality
- 2019
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In: 2019 18TH EUROPEAN CONTROL CONFERENCE (ECC). - : IEEE. - 9783907144008 ; , s. 4270-4275
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Conference paper (peer-reviewed)abstract
- In this paper we show that chordal structure can be used to devise efficient optimization methods for robust model predictive control problems. To this end, first the problem is converted to an equivalent robust quadratic programming formulation. We then illustrate how the chordal structure can be used to distribute the computations in a primal-dual interior-point method among computational agents, which in turn allows us to accelerate the algorithm by efficient parallel computations. We investigate performance of the framework in Julia using numerical examples.
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| 4. |
- Ahmadi, Shervin Parvini, 1989-, et al.
(author)
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Parallel Exploitation for Tree-Structured Coupled Quadratic Programming in Julia
- 2018
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In: Proceedings of the 22nd International Conference on System Theory, Control and Computing. - : IEEE. - 9781538644447 - 9781538644430 - 9781538644454 ; , s. 597-602
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Conference paper (peer-reviewed)abstract
- The main idea in this paper is to implement a distributed primal-dual interior-point algorithm for loosely coupled Quadratic Programming problems. We implement this in Julia and show how can we exploit parallelism in order to increase the computational speed. We investigate the performance of the algorithm on a Model Predictive Control problem.
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| 5. |
- Andersen, Martin, et al.
(author)
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Distributed Robust Stability Analysis of Interconnected Uncertain Systems
- 2012
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In: Proceedings of the 51st IEEE Conference on Decision and Control. - 0743-1546. - 9781467320641 - 9781467320658 ; , s. 1548-1553
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Conference paper (peer-reviewed)abstract
- This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This approach yields a sparse linear matrix inequality which can be decomposed into a set of smaller, coupled linear matrix inequalities. This allows us to solve the analysis problem efficiently and in a distributed manner. We also show that the decomposed problem is equivalent to the original robustness analysis problem, and hence our method does not introduce additional conservativeness.
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| 6. |
- Andersen, Martin S., et al.
(author)
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Robust Stability Analysis of Sparsely Interconnected Uncertain Systems
- 2014
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In: IEEE Transactions on Automatic Control. - : IEEE. - 0018-9286 .- 1558-2523. ; 59:8, s. 2151-2156
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Journal article (peer-reviewed)abstract
- In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.
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| 7. |
- Ankelhed, Daniel, et al.
(author)
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A Partially Augmented Lagrangian Method for Low Order H-Infinity Controller Synthesis Using Rational Constraints
- 2011
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Reports (other academic/artistic)abstract
- When designing robust controllers, H-infinity synthesis is a common tool touse. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.The approach used in this work is based on formulating the constraint onthe maximum order of the controller as a polynomial (or rational) equation.This equality constraint is added to the optimization problem of minimizingan upper bound on the H-innity norm of the closed loop system subjectto linear matrix inequality (LMI) constraints. The problem is then solvedby reformulating it as a partially augmented Lagrangian problem where theequality constraint is put into the objective function, but where the LMIsare kept as constraints.The proposed method is evaluated together with two well-known methodsfrom the literature. The results indicate that the proposed method hascomparable performance in most cases, especially if the synthesized con-troller has many parameters, which is the case if the system to be controlledhas many input and output signals.
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| 8. |
- Ankelhed, Daniel, et al.
(author)
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A Partially Augmented Lagrangian Method for Low Order H-Infinity Controller Synthesis Using Rational Constraints
- 2012
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In: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 57:11, s. 2901-2905
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Journal article (peer-reviewed)abstract
- This technical note proposes a method for low order H-infinity synthesis where the constraint on the order of the controller is formulated as a rational equation. The resulting nonconvex optimization problem is then solved by applying a partially augmented Lagrangian method. The proposed method is evaluated together with two well-known methods from the literature. The results indicate that the proposed method has comparable performance and speed.
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| 9. |
- Ankelhed, Daniel, et al.
(author)
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A Primal-Dual Method for Low Order H-Infinity Controller Synthesis
- 2010
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In: Proceedings of Reglermöte 2010. - Lund : Linköping University Electronic Press.
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Conference paper (other academic/artistic)abstract
- When designing robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. By using the fact that the polynomial (or rational) is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex function is to be minimized over a convex set defined by linear matrix inequalities.The proposed method is evaluated together with a well-known method from the literature. The results indicate that the proposed method performs slightly better.
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| 10. |
- Ankelhed, Daniel, et al.
(author)
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A Primal-Dual Method for Low Order H-Infinity Controller Synthesis
- 2009
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In: Proceedings of the 48th IEEE Conference on Decision and Control held jointly with the 28th Chinese Control Conference. - : IEEE. - 9781424438716 - 9781424438723 ; , s. 6674-6679
-
Conference paper (peer-reviewed)abstract
- When designing robust controllers, H-infinity synthesisis a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex,even when the order of the system is low.The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. By using the fact that the polynomial (or rational) is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex function is to be minimized over a convex set defined by linear matrix inequalities.The proposed method is evaluated together with a wellknown method from the literature. The results indicate that the proposed method performs slightly better.
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