# Shape and topology optimization for variational inequalities with pointwise boundary observation

## TL;DR

This paper addresses shape and topology optimization problems involving variational inequalities with unilateral conditions and boundary observations, employing regularization and penalization techniques within the Hamiltonian framework.

## Contribution

It introduces a novel approach combining regularization and penalization methods for variational inequalities in shape and topology optimization.

## Key findings

- Effective numerical examples demonstrate the method's viability.
- The approach successfully handles unilateral boundary conditions.
- The techniques improve the stability and accuracy of the optimization process.

## Abstract

We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to shape/topology optimization problems. Numerical examples are also included.