Open AccessApproximate optimality for quasi approximate solutions in nonsmooth semi-infinite programming problems, using ε-upper semi-regular semi-convexificators
Author(s) -
Jutamas Kerdkaew,
Rabian Wangkeeree,
Gue Lee Myung
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2006073k
Subject(s) - mathematics , quasiconvex function , semi infinite programming , mathematical optimization , upper and lower bounds , mathematical analysis , subderivative , regular polygon , convex optimization , geometry
In this paper, we study optimality conditions of quasi approximate solutions for nonsmooth semi-infinite programming problems (for short, (SIP)), in terms of ?-upper semi-regular semi-convexificator which is introduced here. Some classes of functions, namely (?-?*?)-pseudoconvex functions and (?-?*?)-quasiconvex functions with respect to a given ?-upper semi-regular semi-convexificator are introduced, respectively. By utilizing these new concepts, sufficient optimality conditions of approximate solutions for the nonsmooth (SIP) are established. Moreover, as an application, optimality conditions of quasi approximate weakly efficient solution for nonsmooth multi-objective semi-infinite programming problems (for short, (MOSIP)) are presented.