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Differential stability of convex discrete optimal control problems with possibly empty solution sets

OPTIMIZATION 2022年第7期71卷 1839-1862页

作者： Toan, N. T. Hanoi Univ Sci & Technol Sch Appl Math & Informat Hanoi Vietnam

As a complement to two recent papers by Toan and Yao (Mordukhovich subgradients of the value function to a parametric discrete optimal control problem. J Global Optim. 2014;58:595-612), and by An and Toan (Differential stability of convex discrete optimal control problems. Acta Math Vietnam. 2018;43:201-217) on subdifferentials of the optimal value function of discrete optimal control problems, this paper studies the differential stability of convex discrete optimal control problems under control constraints, where the solution set may be empty. By using a suitable sum rule for epsilon-subdifferentials and a suitable product rule for epsilon-normal directions, we obtain formulas for computing the epsilon-subdifferential of the optimal value function. Several illustrative examples are also given.

关键词： convex discrete optimal control problem optimal value function Conjugate function ϵ -subdifferentials ϵ -normal directions

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Differential Stability Properties of convex Optimization and optimal control problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2024年第2期201卷 609-630页

作者： Toan, Nguyen Thi Thuy, Le Quang Hanoi Univ Sci & Technol Sch Appl Math & Informat 1 Dai Co Viet Hanoi Vietnam

This paper studies the solution stability of convex optimization and discrete convexoptimal control problems in Banach spaces, where the solution set may be *** both the optimization problem and the optimal control problem, formulas forthe epsilon-subdifferential of the optimal value function are derived without qualificationconditions. We first calculate the epsilon-subdifferential of the optimal value function toa parametric optimization problem with geometrical and functional constraints. Wethen use the obtained results to derive a formula for computing the epsilon-subdifferentialof the optimal value function to a discrete convex optimal control problem with linearstate equations, control constraints and initial, terminal conditions

关键词： convex optimization problem convex discrete optimal control problem optimal value function Conjugate function epsilon-subdifferentials epsilon-normal directions

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