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arXiv · 2307.04845

On Pareto equilibria for bi-objective diffusive optimal control problems

Pitágoras P. de Carvalho·Enrique Fernández-Cara·Juan Límaco·Denilson Menezes·Yuri Thamsten
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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.

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Pitágoras P. de Carvalho, Enrique Fernández-Cara, Juan Límaco, Denilson Menezes, Yuri Thamsten. 2023-07-10. On Pareto equilibria for bi-objective diffusive optimal control problems. https://arxiv.org/abs/2307.04845

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