Characterization of properly efficient solutions by generalized scalarization methods

1983 ◽  
Vol 41 (3) ◽  
pp. 491-502 ◽  
Author(s):  
W. B. Gearhart
Keyword(s):  
Efficient Solutions ◽  
Properly Efficient Solutions ◽  
Scalarization Methods

scholarly journals Multiobjective duality with ρ−(η,θ)-invexity

2005 ◽  
Vol 2005 (2) ◽  
pp. 175-180 ◽  
Author(s):  
C. Nahak ◽  
S. Nanda
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Efficient Solutions ◽  
Duality Theorems ◽  
Converse Duality ◽  
Dual Problems ◽  
Properly Efficient Solutions ◽  
Multiobjective Programming Problem ◽  
Primal And Dual Problems ◽  
Primal And Dual

Under ρ−(η,θ)-invexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems for a multiobjective programming problem.

scholarly journals Symmetric duality for Bonvex multiobjective fractional continuous time programming problems

2010 ◽  
Vol 7 (2) ◽  
pp. 413-424
Author(s):  
Deo Brat Ojha
Keyword(s):  
Continuous Time ◽  
Efficient Solutions ◽  
Weak Duality ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Multi Objective ◽  
Properly Efficient Solutions ◽  
Self Duality ◽  
Duality Relations

We introduced a symmetric dual for multi objective fractional variational programs in second order. Under invexity assumptions, we established weak, strong and converse duality as well as self duality relations .We work with properly efficient solutions in strong and converse duality theorems. The weak duality theorems involves efficient solutions .

scholarly journals Efficient Solutions of Interval Programming Problems with Inexact Parameters and Second Order Cone Constraints

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 270
Author(s):  
Ali Sadeghi ◽  
Mansour Saraj ◽  
Nezam Amiri
Keyword(s):  
Objective Function ◽  
Main Idea ◽  
Efficient Solutions ◽  
Second Order ◽  
Interval Programming ◽  
Properly Efficient Solutions ◽  
Cone Constraints ◽  
Second Order Cone ◽  
Convexity Properties ◽  
Interval Valued

In this article, a methodology is developed to solve an interval and a fractional interval programming problem by converting into a non-interval form for second order cone constraints, with the objective function and constraints being interval valued functions. We investigate the parametric and non-parametric forms of the interval valued functions along with their convexity properties. Two approaches are developed to obtain efficient and properly efficient solutions. Furthermore, the efficient solutions or Pareto optimal solutions of fractional and non-fractional programming problems over R + n ⋃ { 0 } are also discussed. The main idea of the present article is to introduce a new concept for efficiency, called efficient space, caused by the lower and upper bounds of the respective intervals of the objective function which are shown in different figures. Finally, some numerical examples are worked through to illustrate the methodology and affirm the validity of the obtained results.

Connectedness of the sets of weak efficient solutions for generalized vector equilibrium problems

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Qing-You Liu ◽  
Xian-Jun Long ◽  
Nan-jing Huang
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Efficient Solutions ◽  
Vector Equilibrium Problem ◽  
Vector Equilibrium Problems ◽  
Generalized Vector Equilibrium Problem ◽  
Generalized Vector Equilibrium Problems ◽  
Vector Equilibrium ◽  
Locally Convex

AbstractIn this paper, a generalized vector equilibrium problem is introduced and studied. A scalar characterization of weak efficient solutions for the generalized vector equilibrium problem is obtained. By using the scalarization result, the existence of the weak efficient solutions and the connectedness of the set of weak efficient solutions for the generalized vector equilibrium problem are proved in locally convex spaces.

Characterizing ϵ-properly efficient solutions

2014 ◽  
Vol 30 (3) ◽  
pp. 583-593 ◽  
Author(s):  
K. Khaledian ◽  
E. Khorram ◽  
B. Karimi
Keyword(s):  
Efficient Solutions ◽  
Properly Efficient Solutions

A saddle point characterization of efficient solutions for interval optimization problems

2017 ◽  
Vol 58 (1-2) ◽  
pp. 193-217 ◽  
Author(s):  
Debdulal Ghosh ◽  
Debdas Ghosh ◽  
Sushil Kumar Bhuiya ◽  
Lakshmi Kanta Patra
Keyword(s):  
Saddle Point ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Interval Optimization
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