pseudoconvex functions
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Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 274 ◽  
Author(s):  
Izhar Ahmad ◽  
Khushboo Verma ◽  
Suliman Al-Homidan

A new mixed type nondifferentiable higher-order symmetric dual programs over cones is formulated. As of now, in the literature, either Wolfe-type or Mond–Weir-type nondifferentiable symmetric duals have been studied. However, we present a unified dual model and discuss weak, strong, and converse duality theorems for such programs under higher-order F - convexity/higher-order F - pseudoconvexity. Self-duality is also discussed. Our dual programs and results generalize some dual formulations and results appeared in the literature. Two non-trivial examples are given to show the uniqueness of higher-order F - convex/higher-order F - pseudoconvex functions and existence of higher-order symmetric dual programs.


Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 2073-2089
Author(s):  
Jutamas Kerdkaew ◽  
Rabian Wangkeeree ◽  
Gue Lee

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.


2019 ◽  
Vol 109 (2) ◽  
pp. 217-229 ◽  
Author(s):  
MOHAMMAD TAGHI NADI ◽  
JAFAR ZAFARANI

We present the second-order necessary and sufficient conditions for quasiconvex and pseudoconvex functions in terms of their second-order regular subdifferentials.


2007 ◽  
Vol 20 ◽  
pp. 138-148 ◽  
Author(s):  
A. Hassouni ◽  
A. Jaddar

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