scholarly journals Necessary Conditions for Suboptimization over the Weakly Efficient Set Associated to Generalized Invex Multiobjective Programming

1996 ◽  
Vol 201 (2) ◽  
pp. 502-515 ◽  
Author(s):  
Xu Zengkun
Keyword(s):  
Multiobjective Programming ◽  
Necessary Conditions ◽  
Efficient Set ◽  
Weakly Efficient Set

Inner approximation algorithms for optimization over the weakly efficient set

1999 ◽  
Vol 32 (2) ◽  
pp. 5915-5920
Author(s):  
Syuuji Yamada ◽  
Tetsuzo Tanino ◽  
Masahiro Inuiguchi
Keyword(s):  
Approximation Algorithms ◽  
Efficient Set ◽  
Inner Approximation ◽  
Weakly Efficient Set

scholarly journals Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Wenyan Han ◽  
Guolin Yu ◽  
Tiantian Gong
Keyword(s):  
Optimality Conditions ◽  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Type I ◽  
Generalized Convex Functions ◽  
Alternative Theorem ◽  
Multiobjective Programming Problem

This note is devoted to the investigation of optimality conditions for robust approximate quasi weak efficient solutions to a nonsmooth uncertain multiobjective programming problem (NUMP). Firstly, under the extended nonsmooth Mangasarian–Fromovitz constrained qualification assumption, the optimality necessary conditions of robust approximate quasi weak efficient solutions are given by using an alternative theorem. Secondly, a class of generalized convex functions is introduced to the problem (NUMP), which is called the pseudoquasi-type-I function, and its existence is illustrated by a concrete example. Finally, under the pseudopseudo-type-I generalized convexity hypothesis, the optimality sufficient conditions for robust approximate quasi weak efficient solutions to the problem (NUMP) are established.

Sign in / Sign up

Export Citation Format

Share Document