A NEW RELAXATION METHOD FOR OPTIMAL CONTROL OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES OBSTACLE PROBLEMS

被引：0

作者：

Osmani, El Hassene ^{[1
,2
]}

Haddou, Mounir ^{[2
]}

Bensalem, Naceurdine ^{[1
]}

机构：

[1] Univ Ferhat Abbas Setif 1, Lab Fundamental & Numer Math, Setif 19000, Algeria

[2] Univ Rennes, INSA Rennes, CNRS, IRMAR UMR 6625, F-35000 Rennes, France

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2023年 / 13卷 / 01期

关键词：

Optimal control; Lagrange multipliers; Variational inequalities; Mathematical programming; Smoothing methods; IPOPT solver; MATHEMATICAL PROGRAMS;

D O I：

10.3934/naco.2021061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first relax the feasible domain of the problem, then using both mathematical programming methods and penalization methods we get optimality conditions with smooth Lagrange multipliers. Some numerical experiments using the Interior Point Optimizer (IPOPT), Nonlinear Interior point Trust Region Optimization (KNITRO) and Sequential Quadratic Optimization Technique (SNOPT) are presented to verify the efficiency of our approach.

引用

页码：169 / 193

页数：25

共 19 条

[1] Optimal control of partial differential equations based on the Variational Iteration Method [J].