Numerical Methods for Nash Equilibria in Multi-objective Control of Processes Governed by Partial Differential Equations

We will discuss numerical solutions of Multi-objective Control problems governed by partial differential equations. More precisely, we will look for Nash Equilibria, which are solutions to non-cooperative differential games. First we will study the continuous case. Then, in order to compute solutions, we will combine finite difference schemes for the time discretization, finite element methods for the space discretization and a conjugate gradient algorithm (or other suitable alternative) for the iterative solution of the discrete differential game. Finally, we will apply this methodology to the solution of several test problems.