On optimal control of free boundary problems of obstacle type

TL;DR

This paper investigates numerical methods for optimal control in shape optimization problems governed by obstacle-type elliptic variational inequalities, comparing BFGS algorithms for non-smooth, non-convex problems.

Contribution

It reformulates a shape optimization problem as a boundary control problem and evaluates BFGS methods for solving the resulting non-smooth, non-convex optimization problem.

Findings

BFGS with inexact line search improves convergence.

Reformulation as boundary control simplifies the shape optimization.

Numerical experiments demonstrate method effectiveness.

Abstract

A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed domain. The discretized optimal control problem is a non-smooth and non-convex mathematical programing problem. The performance of the standard BFGS quasi-Newton method and the BFGS method with the inexact line search are tested.