Locally Lipschitz Stability of Solutions to a Parametric Parabolic Optimal Control Problem with Mixed Pointwise Constraints

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-10-14 DOI:10.1007/s00245-024-10191-w

Huynh Khanh

引用次数: 0

Abstract

A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise constraints. By analyzing regularity and establishing stability condition of Lagrange multipliers we prove that, if the unperturbed problem satisfies the strong second-order sufficient condition, then the solution map and the associated Lagrange multipliers are locally Lipschitz continuous functions of parameters.

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具有混合点式约束条件的参数抛物线优化控制问题解的局部 Lipschitz 稳定性

本文研究了一类由具有混合点约束条件的半线性抛物方程支配的参数最优控制问题。扰动出现在目标函数、状态方程和混合点约束中。通过分析正则性和建立拉格朗日乘数的稳定性条件，我们证明，如果未扰动问题满足强二阶充分条件，那么解映射和相关的拉格朗日乘数是参数的局部利普齐兹连续函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.