Payame Noor University (PNU) Control and Optimization in Applied Mathematics 2383-3130 9 2 2024 12 01 On Constraint Qualifications and Optimality Conditions in‎ ‎Nonsmooth Semi-infinite Optimization 53 66 10985 10.30473/coam.2024.69322.1247 EN Atefeh Hassani Bafrani Department of Mathematics‎, ‎Payame Noor University (PNU)‎, ‎P.O‎. ‎Box 19395-4697‎, ‎Tehran‎, ‎Iran‎‎. Journal Article 2023 11 02 The primary objective of this paper is to enhance several well-known geometric constraint qualifications and necessary optimality conditions for nonsmooth semi-infinite optimization problems (SIPs). We focus on defining novel algebraic Mangasarian-Fromovitz type constraint qualifications, and on presenting two Karush-Kuhn-Tucker type necessary optimality conditions for nonsmooth SIPs defined by locally Lipschitz functions. Then, by employing a new type of generalized invex functions, we present sufficient conditions for the optimality of a feasible point of the considered problems. It is noteworthy that the new class of invex functions we considered encompasses several classes of invex functions introduced previously. Our results are based on the Michel-Penot subdifferential. https://mathco.journals.pnu.ac.ir/article_10985_0bf55ef0d7a599627f9eaf409ae60e61.pdf