scholarly journals WEAK PARETO OPTIMALITY OF MULTIOBJECTIVE PROBLEM IN A BANACH SPACE

10.5109/13145 ◽  
1981 ◽  
Vol 19 (3/4) ◽  
pp. 19-23
Author(s):  
Masayoshi Minami
Keyword(s):  
Banach Space ◽  
Pareto Optimality ◽  
Multiobjective Problem ◽  
Weak Pareto Optimality

Weak Pareto optimality and the approximate support property

1993 ◽  
Vol 22 (1) ◽  
pp. 61-71 ◽  
Author(s):  
Robert A. Becker ◽  
Hari Bercovici ◽  
Ciprian Foias
Keyword(s):  
Pareto Optimality ◽  
Weak Pareto Optimality ◽  
Support Property

scholarly journals A SIMPLE AXIOMATIZATION OF THE EGALITARIAN SOLUTION

2014 ◽  
Vol 16 (04) ◽  
pp. 1450008 ◽  
Author(s):  
ISMAIL SAGLAM
Keyword(s):  
Pareto Optimality ◽  
Weak Pareto Optimality ◽  
Egalitarian Solution ◽  
Interpersonal Utility Comparisons

In this paper, we present a simple axiomatization of the n-person egalitarian solution. The single condition sufficient for characterization is a new axiom, called symmetric decomposability that combines the axioms of step-by-step negotiations, symmetry, and weak Pareto optimality used in an early characterization by Kalai [(1977) Proportional solutions to bargaining situations: Interpersonal utility comparisons, Econometrica45, 1623–1630].

scholarly journals Multiobjective Convex Optimization in Real Banach Space

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2148
Author(s):  
Kin Keung Lai ◽  
Mohd Hassan ◽  
Jitendra Kumar Maurya ◽  
Sanjeev Kumar Singh ◽  
Shashi Kant Mishra
Keyword(s):  
Banach Space ◽  
Multiobjective Optimization ◽  
Saddle Point ◽  
Optimality Conditions ◽  
Pareto Optimality ◽  
Real Banach Space ◽  
Optimization Problems ◽  
Mixed Integer ◽  
Multiobjective Optimization Problems ◽  
Necessary And Sufficient

In this paper, we consider convex multiobjective optimization problems with equality and inequality constraints in real Banach space. We establish saddle point necessary and sufficient Pareto optimality conditions for considered problems under some constraint qualifications. These results are motivated by the symmetric results obtained in the recent article by Cobos Sánchez et al. in 2021 on Pareto optimality for multiobjective optimization problems of continuous linear operators. The discussions in this paper are also related to second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones due to Mishra and Wang in 2005. Further, we establish Karush–Kuhn–Tucker optimality conditions using saddle point optimality conditions for the differentiable cases and present some examples to illustrate our results. The study in this article can also be seen and extended as symmetric results of necessary and sufficient optimality conditions for vector equilibrium problems on Hadamard manifolds by Ruiz-Garzón et al. in 2019.

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