scholarly journals Optimality and duality for complex multi-objective programming

2022 ◽  
Vol 12 (1) ◽  
pp. 121
Author(s):  
Tone-Yau Huang ◽  
Tamaki Tanaka
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Efficient Solutions ◽  
Dual Model ◽  
Duality Theorems ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Optimality And Duality ◽  
Objective Programming

<p style='text-indent:20px;'>We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.</p>

scholarly journals Optimality and duality for nonsmooth semi-infinite E-convex multi-objective programming with support functions

2020 ◽  
Vol 11 ◽  
pp. 17
Author(s):  
Tarek Emam
Keyword(s):  
Strong Duality ◽  
Sufficient Optimality Conditions ◽  
Convex Programming Problem ◽  
Duality Theorems ◽  
Support Functions ◽  
Primal Problem ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Optimality And Duality ◽  
Convexity Assumptions

In this paper, we study a nonsmooth semi-infinite multi-objective E-convex programming problem involving support functions. We derive sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak and strong duality theorems under various generalized E-convexity assumptions.

A Necessary Condition for Optimality in Multi Objective Programming under Inclusion Constraints

2011 ◽  
Vol 403-408 ◽  
pp. 1322-1325
Author(s):  
Jin Xing Shen
Keyword(s):  
Optimality Conditions ◽  
Optimality Condition ◽  
Pareto Optimality ◽  
Necessary Condition ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Objective Programming ◽  
Single Objective

Optimality conditions for multi objective programming problems have been studied extensively in the literature. A necessary condition for Pareto optimality is derived by reducing the multi objective programming under inclusion constraints to systems of single objective problem and then using known results of them. The result is reasonable and efficient. Our aim in this paper is to get the optimality condition of problem (MOP) by a lemma which helps reducing multi objective optimality problem to systems of single objective ones.

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