A new Relaxation Method for Optimal Control of Semilinear Elliptic Variational Inequalities Obstacle Problems

2020/07/09 by El Hassene Osmani, Osmani, El Hassene, Mounir Haddou +3
Computer Science · Mathematics · #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2007.04602

openalex publication_date 2020/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 IPOPT algorithm are presented to verify the efficiency of our approach.

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