Necessary Optimality Conditions for Non-smooth Continuous-Time Problems Using Convexificators

In this paper, we develop general necessary optimality conditions of the KKT types for non-smooth continuous-time optimization problems with inequality constraints. The primary instrument in our study is the concept of a convexificator. Based on this concept, non-smooth versions of the Mangasarian-Fromovitz constraint qualification are presented. Then, we derive optimality conditions for this problem under weak assumptions. Indeed, the constraint functions and the objective function that exist in this problem are not necessarily differentiable or convex.