Optimality Conditions of the Approximate Efficiency for Nonsmooth Robust Multiobjective Fractional Semi-Infinite Optimization Problems

This paper is devoted to the investigation of optimality conditions and saddle point theorems for robust approximate quasi-weak efficient solutions for a nonsmooth uncertain multiobjective fractional semi-infinite optimization problem (NUMFP). Firstly, a necessary optimality condition is established...

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Bibliographic Details
Published in:Axioms Vol. 12; no. 7; p. 635
Main Authors: Gao, Liu, Yu, Guolin, Han, Wenyan
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.07.2023
Subjects:
approximate solution
Euclidean space
generalized convexity
Mathematical optimization
Mathematical research
multiobjective semi-infinite optimization
Multiple objective analysis
optimality conditions
Optimization
Robustness
saddle point
Saddle points
Theorems
China
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:This paper is devoted to the investigation of optimality conditions and saddle point theorems for robust approximate quasi-weak efficient solutions for a nonsmooth uncertain multiobjective fractional semi-infinite optimization problem (NUMFP). Firstly, a necessary optimality condition is established by using the properties of the Gerstewitz’s function. Furthermore, a kind of approximate pseudo/quasi-convex function is defined for the problem (NUMFP), and under its assumption, a sufficient optimality condition is obtained. Finally, we introduce the notion of a robust approximate quasi-weak saddle point to the problem (NUMFP) and prove corresponding saddle point theorems.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12070635