%0 Journal Article %T Necessary Optimality Conditions for Non-smooth Continuous-Time Problems‎ ‎Using Convexificators %J Control and Optimization in Applied Mathematics %I Payame Noor University (PNU) %Z 2383-3130 %A Ansari Ardali, Ali %D 2020 %\ 01/01/2020 %V 5 %N 1 %P 1-13 %! Necessary Optimality Conditions for Non-smooth Continuous-Time Problems‎ ‎Using Convexificators %K Continuous-time problems‎ %K ‎Optimality conditions‎ %K ‎Upper semi-regular convexificator‎ %K ‎Non-smooth analysis %R 10.30473/coam.2021.56443.1154 %X 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. %U https://mathco.journals.pnu.ac.ir/article_7861_055827b33807ddc36e8eeee5cee9e2e3.pdf