Numerical methods for Nash equilibria in multiobjective control of partial differential equations

Abstract

This paper is concerned with the numerical solution of multiobjective control problems associated with linear (resp., nonlinear) partial differential equations. More precisely, for such problems, we look for Nash equilibria, which are solutions to noncooperative games. First, we study the continuous case. Then, to compute the solution of the problem, we combine finite-difference methods for the time discretization, finite-element methods for the space discretization, and conjugate gradient algorithms (resp., a suitable algorithm) for the iterative solution of the discrete control problems. Finally, we apply the above methodology to the solution of several tests problems.