This paper deals with the numerical implementation of a systematic method for solving bi-objective optimal control problems for wave equations. More precisely, we look for Nash and Pareto equilibria which respectively correspond to appropriate noncooperative and cooperative strategies in multi-objective optimal control. The numerical methods described here consist of a combination of the following: finite element techniques for space approximation; finite difference schemes for time discretization; gradient algorithms for the solution of the discrete control problems. The efficiency of the computational methods is illustrated by the results of some numerical experiments.

中文翻译：

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关于波动方程某些双目标控制问题的纳什和帕累托平衡计算

本文探讨了一种求解波动方程双目标最优控制问题的系统方法的数值实现。更确切地说，我们寻找Nash和Pareto均衡，它们分别对应于多目标最优控制中的适当非合作和合作策略。这里描述的数值方法由以下各项的组合组成：用于空间逼近的有限元技术；时间离散的有限差分方案；解决离散控制问题的梯度算法。一些数值实验的结果说明了计算方法的效率。