A proximal point algorithm for control approximation problems

The authors consider the optimization problem , which is an extension of a problem studied by Idrissi, Lefebvre and Michelot. This class of problems contains many practically important special cases so as approximation, location and optimal control problems, perturbed linear programming problems and surrogate problems for linear programming. Necessary and sufficient optimality conditions are derived using the sub-differential calculus. A proximal point algorithm is modified by the method of partial inverse in order to solve the optimality condition.