Payame Noor University (PNU) Control and Optimization in Applied Mathematics 2383-3130 3 2 2018 01 01 A General Scalar-Valued Gap Function for Nonsmooth Multiobjective Semi-Infinite Programming یک تابع شکاف حقیقی مقدار برای مسائل برنامه ریزی چند هدفی نیمه نامتناهی غیر هموار 13 26 6719 10.30473/coam.2019.45495.1110 EN Ahmad Rezayi Department of Mathematics‎, ‎Payame Noor University, ‎P.O‎. ‎Box‎. ‎19395-3697‎, ‎Tehran‎, ‎Iran Journal Article 2019 04 14 For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints‎, ‎we define a new gap function that generalizes the definitions of this concept in other articles‎. ‎Then‎, ‎we characterize the efficient‎, ‎weakly efficient‎, ‎and properly efficient solutions of the problem utilizing this new gap function‎. ‎Our results are based on $(\Phi,\rho)-$invexity‎, ‎defined by Clarke subdifferential. ‎Semi-Infinite Programming‎ ‎Multiobjective optimization‎ ‎Constraint qualification‎ ‎Optimality conditions‎ ‎Gap function https://mathco.journals.pnu.ac.ir/article_6719_59f10887b88b535008100a8c10d94722.pdf