scholarly journals Generalized Convexity in Multiobjective Programming

1999 ◽  
Vol 233 (1) ◽  
pp. 205-220 ◽  
Author(s):  
R. Osuna-Gómez ◽  
A. Beato-Moreno ◽  
A. Rufian-Lizana
Keyword(s):  
Generalized Convexity ◽  
Multiobjective Programming

Invex Functions and Generalized Convexity in Multiobjective Programming

1998 ◽  
Vol 98 (3) ◽  
pp. 651-661 ◽  
Author(s):  
R. Osuna-Gómez ◽  
A. Rufián-Lizana ◽  
P. Ruíz-Canales
Keyword(s):  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Invex Functions

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.

Generalized convexity and efficiency for non-regular multiobjective programming problems with inequality-type constraints

2010 ◽  
Vol 73 (8) ◽  
pp. 2463-2475 ◽  
Author(s):  
Beatriz Hernández-Jiménez ◽  
Rafaela Osuna-Gómez ◽  
Manuel Arana-Jiménez ◽  
Gabriel Ruiz Garzón
Keyword(s):  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Multiobjective Programming Problems ◽  
Inequality Type

scholarly journals E-invexity and generalized E-invexity in E-differentiable multiobjective programming

2019 ◽  
Vol 24 ◽  
pp. 01002 ◽  
Author(s):  
Najeeb Abdulaleem
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Differentiable Function ◽  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Vector Optimization Problems ◽  
Invex Functions ◽  
Differentiable Vector

In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems. For an E-differentiable function, the concept of E-invexity is introduced as a generalization of the E-differentiable E-convexity notion. In addition, some properties of E-differentiable E-invex functions are investigated. Furthermore, the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable vector optimization problems with both inequality and equality constraints. Also, the sufficiency of the E-Karush-Kuhn-Tucker necessary optimality conditions are proved for such E-differentiable vector optimization problems in which the involved functions are E-invex and/or generalized E-invex.

scholarly journals Optimality and duality for nonsmooth semi-infinite multiobjective programming with support functions

2017 ◽  
Vol 27 (2) ◽  
pp. 205-218 ◽  
Author(s):  
Yadvendra Singh ◽  
S.K. Mishra ◽  
K.K. Lai
Keyword(s):  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Support Functions ◽  
Primal Problem ◽  
Special Cases ◽  
Multiobjective Programming Problem ◽  
Optimality And Duality ◽  
Convexity Assumptions

In this paper, we consider a nonsmooth semi-infinite multiobjective programming problem involving support functions. We establish sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak, strong and strict converse duality theorems under various generalized convexity assumptions. Moreover, some special cases of our problem and results are presented.

Saddle point criteria in semi-infinite minimax fractional programming under (Φ,ρ)-invexity

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2557-2574 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Saddle Point ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Equality Constraints ◽  
New Class ◽  
Minimax Fractional Programming

Semi-infinite minimax fractional programming problems with both inequality and equality constraints are considered. The sets of parametric saddle point conditions are established for a new class of nonconvex differentiable semi-infinite minimax fractional programming problems under(?,?)-invexity assumptions. With the reference to the said concept of generalized convexity, we extend some results of saddle point criteria for a larger class of nonconvex semi-infinite minimax fractional programming problems in comparison to those ones previously established in the literature.

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