Optimality Conditions for Non-Smooth Multi Objective Semi-Infinite Programming

2013 ◽  
pp. 467-474
Author(s):  
Xiaoyan Gao
Keyword(s):  
Optimality Conditions ◽  
Multi Objective ◽  
Infinite Programming

scholarly journals Approximate optimality for quasi approximate solutions in nonsmooth semi-infinite programming problems, using ε-upper semi-regular semi-convexificators

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 2073-2089
Author(s):  
Jutamas Kerdkaew ◽  
Rabian Wangkeeree ◽  
Gue Lee
Keyword(s):  
Optimality Conditions ◽  
Efficient Solution ◽  
Approximate Solutions ◽  
Sufficient Optimality Conditions ◽  
Quasiconvex Functions ◽  
Weakly Efficient Solution ◽  
Multi Objective ◽  
New Concepts ◽  
Pseudoconvex Functions ◽  
Infinite Programming

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.

scholarly journals A note on the paper "Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming"

2020 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Aissam Ichatouhane
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Optimality Condition ◽  
Short Proof ◽  
Necessary Optimality Condition ◽  
Main Result Theorem ◽  
Correct Formulation ◽  
Result Theorem ◽  
Infinite Programming ◽  
Interval Valued

A nonsmooth semi-infinite interval-valued vector programming problem is solved in the paper by Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020066, 2020). The necessary optimality condition obtained by the authors, as well as its proof, is false. Some counterexamples are given to refute some results on which the main result (Theorem 4.5) is based. For the convinience of the reader, we correct the faulty in those results, propose a correct formulation of Theorem 4.5 and give also a short proof.

scholarly journals Optimality conditions and duality for multiobjective semi-infinite programming with data uncertainty via Mordukhovich subdifferential

2021 ◽  
pp. 13-13
Author(s):  
Thanh-Hung Pham
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Data Uncertainty ◽  
Mordukhovich Subdifferential ◽  
New Concepts ◽  
Infinite Programming

Based on the notation of Mordukhovich subdifferential in [27], we propose some of new concepts of convexity to establish optimality conditions for quasi ?-solutions for nonlinear semi-infinite optimization problems with data uncertainty in constraints. Moreover, some examples are given to illustrate the obtained results.

Optimality conditions for convex semi-infinite programming problems

1980 ◽  
Vol 27 (3) ◽  
pp. 413-435 ◽  
Author(s):  
A. Ben-Tal ◽  
L. Kerzner ◽  
S. Zlobec
Keyword(s):  
Optimality Conditions ◽  
Infinite Programming
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