Minimax control of nonlinear evolution equations

摘要

In this paper we study nonlinear parametric optimal control problems. We formulate the relevant minimax problem and prove the existence of an optimal control. Also we derive necessary conditions for saddle point optimality. We also associate to the original optimization problem a dual problem and then for the pair we prove a complete duality theorem. Finally we present two examples of parabolic distributed parameter systems, which illustrate the abstract results.