An exact penalty method for constrained optimal control problems

Hammoudi, Abdelwahhab; Benharrat, Mohammed

doi:10.1007/s12215-020-00496-4

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…Various necessary and/or sufficient conditions for the local exactness of penalty functions for optimal control problems and some closely related results can be found in Refs. [11][12][13]19,21,35,42,85,86]. Typically, one needs to impose a suitable constraint qualification at a given point to ensure that the corresponding penalty function for an optimal control problem under consideration is locally exact.…”

Section: Optimality Conditionsmentioning

confidence: 99%

“…Local properties of exact penalty functions for optimal control problems with state constraints were first studied by Lasserre [42], and Xing et al [85,86]. Global properties of exact penalty functions were studied for free-endpoint problems by Demyanov et al [11][12][13], problems with state inequality constrains by Hammoudi and Benharrat [35], and problems for some implicit control systems by Demyanov et al [14]. A general theory of exact penalty functions for optimal control problems was developed by Dolgopolik et al [19,21].…”

Section: Introductionmentioning

confidence: 99%

“…2.2.5 and 4.5.4), there exists a subsequence of the sequence {V ′ l } that converges to V * 0 almost everywhere on [0, T ]. Hence passing to the limit in inequality (35) along the corresponding subsequence one finally gets that…”

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confidence: 95%

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An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints

Долгополик¹

2023

Preprint

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A class of exact penalty-type local search methods for optimal control problems with nonsmooth cost functional, nonsmooth (but continuous) dynamics, and nonsmooth state and control constraints is presented, in which the the penalty parameter and several line search parameters are adaptively adjusted during the optimisation process. This class of methods is applicable to problems having a known DC (Differenceof-Convex functions) structure and in its core is based on the classical DCA method, combined with the steering exact penalty rules for updating the penalty parameter and an adaptive nonmonotone line search procedure. Under the assumption that all auxiliary subproblems are solved only approximately (that is, with finite precision), we prove the correctness of the proposed family of methods and present its detailed convergence analysis. The performance of several different versions of the method is illustrated by means of a numerical example, in which the methods are applied to a semi-academic optimal control problem with a nonsmooth nonconvex state constraint.

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Section: Optimality Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints

Долгополик¹

2023

Preprint

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Collision Avoidance Trajectory Planning of Cluster Spacecraft Considering Energy Optimization

Zhao,

Yin,

Tan

et al. 2024

Lecture Notes in Electrical Engineering

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Pattern-Multiplicative Average of Nonnegative Matrices: When a Constrained Minimization Problem Requires Versatile Optimization Tools

2022

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Given several nonnegative matrices with a single pattern of allocation among their zero/nonzero elements, the average matrix should have the same pattern as well. This is the first tenet of the pattern-multiplicative average (PMA) concept, while the second one suggests the multiplicative nature of averaging. The concept of PMA was motivated in a number of application fields, of which we consider the matrix population models and illustrate solving the PMA problem with several sets of model matrices calibrated in particular botanic case studies. The patterns of those matrices are typically nontrivial (they contain both zero and nonzero elements), the PMA problem thus having no exact solution for a fundamental reason (an overdetermined system of algebraic equations). Therefore, searching for the approximate solution reduces to a constrained minimization problem for the approximation error, the loss function in optimization terms. We consider two alternative types of the loss function and present a general algorithm of searching the optimal solution: basin-hopping global search, then local descents by the method of conjugate gradients or that of penalty functions. Theoretical disadvantages and practical limitations of both loss functions are discussed and illustrated with a number of practical examples.

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An exact penalty method for constrained optimal control problems

Cited by 3 publications

References 26 publications

An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints

An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints

Collision Avoidance Trajectory Planning of Cluster Spacecraft Considering Energy Optimization

Pattern-Multiplicative Average of Nonnegative Matrices: When a Constrained Minimization Problem Requires Versatile Optimization Tools

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