The Karush-Kuhn-Tucker optimality conditions for multi-objective programming problems with fuzzy-valued objective functions

2009 ◽  
Vol 8 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Hsien-Chung Wu
Keyword(s):  
Optimality Conditions ◽  
Objective Functions ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Objective Programming

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.

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 Improved Weighted Sum Multi Objective Programming

2021 ◽  
Vol 7 (01) ◽  
pp. 111-113
Author(s):  
Chandra Sen
Keyword(s):  
Objective Function ◽  
Weighted Sum ◽  
Objective Functions ◽  
Improved Method ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Objective Programming

Optimizing the combined objective function is the most common approach of Multi Objective Programming (MOP). The scalaization of objective functions have been recommended for combining the objective functions of various dimensions. The Weighted Sum Multi Objective Programming (WSMOP) has also been used for obtaining desirable solution. Several WSMOP methods are used for solving multi objective problems. Few weaknesses have noticed in WSMOP methods. An improved method of WSMOP is proposed in the present study for obtaining desirable solution of multi objective programming problems.

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