On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Nash equilibria for the multiobjective control of linear partial differential equations
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
Nash equilibria for the multiobjective control of linear partial differential equations
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
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This article is concerned with the numerical solution of multiobjective control problems associated with nonlinear partial differential equations and more precisely the Burgers equation. For this kind of problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. To compute the solution of the problem, we use a combination of finite-difference methods for the time discretization, finite-element methods for the space discretization, and a quasi-Newton BFGS algorithm for the iterative solution of the discrete control problem. Finally, we apply the above methodology to the solution of several tests problems. To be able to compare our results with existing results in the literature, we discuss first a single-objective control problem, already investigated by other authors. Finally, we discuss the multiobjective case.