Alpaqa: A matrix-free solver for nonlinear MPC and large-scale nonconvex optimization

Pieter, Pas,; Schuurmans, Mathijs; Patrinos, Panagiotis

doi:10.48550/arxiv.2112.02370

Cited by 4 publications

(9 citation statements)

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“…7] proposes to adapt the PG stepsize γ k within the linesearch on the update direction. As recently showcased in [21], not only does this conservatism prove beneficial in preventing the acceptance of poor quality directions, but it often also reduces the overall computational cost. Although numerical simulations indicate superior performance, this refined linesearch lacks a theoretical analysis of its convergence properties.…”

Section: Panoc + : the "Good" Adaptive Stepsize Rulementioning

confidence: 99%

“…These findings will significantly impact on PANOC (+) both in performance and applicability, propagating to all its dependencies, e.g.,by removing stringent assumptions of general purpose optimization solvers such as OpEn [29]. Indeed, the significance and effectiveness of PANOC + have already been demonstrated in [12,21]. As part of the open-source Julia package ProximalAlgorithms.jl [31], our implementation PANOCplus of PANOC + is publicly available.…”

Section: Introductionmentioning

confidence: 99%

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Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity

Marchi

Themelis

2022

J Optim Theory Appl

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Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local Lipschitz gradient continuity for the smooth part of the objective function. We investigate an adaptive scheme for PANOC-type methods (Stella et al. in Proceedings of the IEEE 56th CDC, 2017), namely accelerated linesearch algorithms requiring only the simple oracle of proximal gradient. While including the classical proximal gradient method, our theoretical results cover a broader class of algorithms and provide convergence guarantees for accelerated methods with possibly inexact computation of the proximal mapping. These findings have also significant practical impact, as they widen scope and performance of existing, and possibly future, general purpose optimization software that invoke PANOC as inner solver.

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Section: Panoc + : the "Good" Adaptive Stepsize Rulementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity

Marchi

Themelis

2022

J Optim Theory Appl

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show abstract

“…7] proposes to adapt the PG stepsize γ k within the linesearch on the update direction. As recently showcased in [20], not only does this conservatism prove beneficial in preventing the acceptance of poor quality directions, but it often also reduces the overall computational cost. Although numerical simulations indicate superior performance, this refined linesearch lacks a theoretical analysis of its convergence properties.…”

Section: Panoc + : the "Good" Adaptive Stepsize Rulementioning

confidence: 99%

“…and go back to step 2.3 2.7: k ← k + 1 and start the next iteration at step 2.1 [27,19,20] on two aspects: the adaptive linesearch is shown to terminate, and can cope with a merely locally Lipschitz-differentiable term f . These findings are of high significance also for other methods that rely on PANOC as internal solver, such as the general purpose OpEn [25].…”

Section: Panoc + : the "Good" Adaptive Stepsize Rulementioning

confidence: 99%

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Proximal Gradient Algorithms under Local Lipschitz Gradient Continuity: A Convergence and Robustness Analysis of PANOC

De Marchi,

Themelis

2021

Preprint

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Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local Lipschitz gradient continuity for the smooth part of the objective function. We investigate an adaptive scheme for PANOC-type methods (Stella et al. in Proceedings of the IEEE 56th CDC, 1939-1944, namely accelerated linesearch algorithms requiring only the simple oracle of proximal gradient. While including the classical proximal gradient method, our theoretical results cover a broader class of algorithms and provide convergence guarantees for accelerated methods with possibly inexact computation of the proximal mapping. These findings have also significant practical impact, as they widen scope and performance of existing, and possibly future, general purpose optimization software that invoke PANOC as inner solver. Keywords. Nonsmooth nonconvex optimization • locally Lipschitz gradient • forward-backward splitting • linesearch methods AMS subject classifications. 49J52 • 65K05 • 90C30 * A. Themelis acknowledges the support of the Japan Society for the Promotion of Science (JSPS) KAKENHI grant JP21K17710.

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Learning MPC for Interaction-Aware Autonomous Driving: A Game-Theoretic Approach

Evens

Schuurmans

Patrinos

2022

2022 European Control Conference (ECC)

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We consider the problem of interaction-aware motion planning for automated vehicles in general traffic situations. We model the interaction between the controlled vehicle and surrounding road users using a generalized potential game, in which each road user is assumed to minimize a common cost function subject to shared (collision avoidance) constraints. We propose a quadratic penalty method to deal with the shared constraints and solve the resulting optimal control problem online using an Augmented Lagrangian method based on PANOC. Secondly, we present a simple methodology for learning preferences and constraints of other road users online, based on observed behavior. Through extensive simulations in a highway merging scenario, we demonstrate the practical efficacy of the overall approach as well as the benefits of the proposed online learning scheme.

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Alpaqa: A matrix-free solver for nonlinear MPC and large-scale nonconvex optimization

Cited by 4 publications

References 0 publications

Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity

Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity

Proximal Gradient Algorithms under Local Lipschitz Gradient Continuity: A Convergence and Robustness Analysis of PANOC

Learning MPC for Interaction-Aware Autonomous Driving: A Game-Theoretic Approach

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