A dynamical method for optimal control of the obstacle problem

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2023-05-31 DOI:10.1515/jiip-2020-0135

Qinghua Ran, Xiaoliang Cheng, R. Gong, Ye Zhang

引用次数: 0

Abstract

Abstract In this paper, we consider the numerical method for an optimal control problem governed by an obstacle problem. An approximate optimization problem is proposed by regularizing the original non-differentiable constrained problem with a simple method. The connection between the two formulations is established through some convergence results. A sufficient condition is derived to decide whether a solution of the first-order optimality system is a global minimum. The method with a second-order in time dissipative system is developed to solve the optimality system numerically. Several numerical examples are reported to show the effectiveness of the proposed method.

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障碍物问题最优控制的一种动力学方法

摘要本文研究了一类由障碍物控制的最优控制问题的数值求解方法。用一种简单的方法对原不可微约束问题进行正则化，提出了近似优化问题。通过一些收敛结果，建立了两个公式之间的联系。导出了判定一阶最优系统解是否为全局最小值的一个充分条件。提出了二阶时间耗散系统最优性的数值求解方法。算例表明了该方法的有效性。

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

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography