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.