Karush-Kuhn-Tucker Conditions for Nonsmooth Mathematical Programming Problems in Function Spaces

Lagrange multiplier rules for abstract optimization problems with mixed smooth and convex terms in the cost, with smooth equality constrained and convex inequality constraints are presented. The typical case for the equality constraints that the theory is meant for is given by differential equations. Applications are given to L-minimum norm control problems, L∞norm minimization, and a class of optimal control problems with distributed state constraints and non-smooth cost.