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<p>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 conflictive) 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 with several experiments.</p>

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On Pareto Equilibria for Some Bi-Objective Optimal Control Problems

  • 期刊论文

  • 发表日期：

    2025年6月10日

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  • P. P. de Carvalho,
  • E. Fernández-Cara,
  • J. Límaco,
  • D. Menezes,
  • Y. Thamsten

摘要

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 conflictive) 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 with several experiments.