On Pareto equilibria for bi-objective diffusive optimal control problems
Optimization and Control
2023-07-12 v1 Analysis of PDEs
Abstract
We investigate Pareto equilibria for bi-objective optimal control problems. Our framework comprises the situation in which an agent acts with a distributed control in a portion of a given domain, and aims to achieve two distinct (possibly conflicting) targets. We analyze systems governed by linear and semilinear heat equations and also systems with multiplicative controls. We develop numerical methods relying on a combination of finite elements and finite differences. We illustrate the computational methods we develop via numerous experiments.
Cite
@article{arxiv.2307.04845,
title = {On Pareto equilibria for bi-objective diffusive optimal control problems},
author = {Pitágoras P. de Carvalho and Enrique Fernández-Cara and Juan Límaco and Denilson Menezes and Yuri Thamsten},
journal= {arXiv preprint arXiv:2307.04845},
year = {2023}
}