scholarly journals A Note on Continuity of Solution Set for Parametric Weak Vector Equilibrium Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Pakkapon Preechasilp ◽  
Rabian Wangkeeree
Keyword(s):  
Equilibrium Problem ◽  
Vector Optimization ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Vector Equilibrium Problem ◽  
Vector Optimization Problems ◽  
Vector Equilibrium Problems ◽  
Vector Equilibrium ◽  
Weak Vector

We consider the parametric weak vector equilibrium problem. By using a weaker assumption of Peng and Chang (2014), the sufficient conditions for continuity of the solution mappings to a parametric weak vector equilibrium problem are established. Examples are provided to illustrate the essentialness of imposed assumptions. As advantages of the results, we derive the continuity of solution mappings for vector optimization problems.

scholarly journals LOWER SEMICONTINUITY OF PARAMETRIC GENERALIZED WEAK VECTOR EQUILIBRIUM PROBLEMS

2009 ◽  
Vol 81 (1) ◽  
pp. 85-95 ◽  
Author(s):  
SHENG-JIE LI ◽  
HUI-MIN LIU ◽  
CHUN-RONG CHEN
Keyword(s):  
Equilibrium Problem ◽  
Lower Semicontinuity ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Vector Equilibrium Problems ◽  
Solution Mapping ◽  
Scalarization Method ◽  
Set Valued Mappings ◽  
Vector Equilibrium ◽  
Weak Vector

AbstractIn this paper, using a scalarization method, we obtain sufficient conditions for the lower semicontinuity and continuity of the solution mapping to a parametric generalized weak vector equilibrium problem with set-valued mappings.

Optimality Conditions for Vector Equilibrium Problems with Set-Valued Mappings and Cone Constraints

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
Adela Capătă
Keyword(s):  
Optimality Conditions ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Vector Equilibrium Problem ◽  
Cone Constraints ◽  
Quasi Relative Interior ◽  
Vector Equilibrium ◽  
Necessary And Sufficient

AbstractThe purpose of this paper is to establish necessary and sufficient conditions for a point to be solution of a vector equilibrium problem with setvalued mappings and cone constraints. Using a separation theorem which involves the quasi-relative interior of a convex set, we obtain optimality conditions for solutions of the considered vector equilibrium problem. The main theorem recovers an earlier established result. Then, the results are applied to vector optimization problems and to Stampacchia vector variational inequalities with cone constraints.

scholarly journals Existence Results for New Weak and Strong Mixed Vector Equilibrium Problems on Noncompact Domain

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Ali Farajzadeh ◽  
Kasamsuk Ungchittrakool ◽  
Apisit Jarernsuk
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Vector Variational Inequality ◽  
Vector Equilibrium Problem ◽  
Variational Inequality Problems ◽  
Vector Equilibrium Problems ◽  
Noncompact Domain ◽  
Vector Equilibrium

We introduce and consider two new mixed vector equilibrium problems, that is, a new weak mixed vector equilibrium problem and a new strong mixed vector equilibrium problem which are combinations of certain vector equilibrium problems, and vector variational inequality problems. We prove existence results for the problems in noncompact setting.

Lagrange Multiplier Rules for Weakly Minimal Solutions of Compact-Valued Set Optimization Problems

2019 ◽  
Vol 36 (04) ◽  
pp. 1950021
Author(s):  
Tijani Amahroq ◽  
Abdessamad Oussarhan
Keyword(s):  
Optimality Conditions ◽  
Lagrange Multiplier ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Set Optimization ◽  
Vector Equilibrium Problems ◽  
Multiplier Rules ◽  
Convexity Assumption ◽  
Vector Equilibrium ◽  
Weak Vector

Optimality conditions are established in terms of Lagrange–Fritz–John multipliers as well as Lagrange–Kuhn–Tucker multipliers for set optimization problems (without any convexity assumption) by using new scalarization techniques. Additionally, we indicate how these results may be applied to some particular weak vector equilibrium problems.

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.

scholarly journals Existence and Duality of Generalized ε-Vector Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hong-Yong Fu ◽  
Bin Dan ◽  
Xiang-Yu Liu
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Equilibrium Problem ◽  
Vector Equilibrium Problems ◽  
Kkm Theorem ◽  
Special Cases ◽  
Primal And Dual Problems ◽  
Primal And Dual ◽  
Vector Equilibrium

We consider a generalized ε-vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem, we obtain some existence theorems for the generalized ε-vector equilibrium problem. We also investigate the duality of this generalized ε-vector equilibrium problem and discuss the equivalence relation between solutions of primal and dual problems.

scholarly journals Extended Mixed Vector Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Mijanur Rahaman ◽  
Adem Kılıçman ◽  
Rais Ahmad
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Vector Equilibrium Problem ◽  
Vector Spaces ◽  
Vector Equilibrium Problems ◽  
Topological Vector Spaces ◽  
Fan Theorem ◽  
Noncompact Domain ◽  
Vector Equilibrium

We study extended mixed vector equilibrium problems, namely, extended weak mixed vector equilibrium problem and extended strong mixed vector equilibrium problem in Hausdorff topological vector spaces. Using generalized KKM-Fan theorem (Ben-El-Mechaiekh et al.; 2005), some existence results for both problems are proved in noncompact domain.

scholarly journals Optimality Conditions forε-Vector Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Lu Wei-zhong ◽  
Huang Shou-jun ◽  
Yang Jun
Keyword(s):  
Equilibrium Problem ◽  
Convex Sets ◽  
Equilibrium Problems ◽  
Vector Equilibrium Problem ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Vector Equilibrium Problems ◽  
Necessary And Sufficient Condition ◽  
Vector Equilibrium ◽  
Necessary And Sufficient

By virtue of the separation theorem of convex sets, a necessary condition and a sufficient condition forε-vector equilibrium problem with constraints are obtained. Then, by using the Gerstewitz nonconvex separation functional, a necessary and sufficient condition forε-vector equilibrium problem without constraints is obtained.

scholarly journals A primal-dual approach of weak vector equilibrium problems

2018 ◽  
Vol 16 (1) ◽  
pp. 276-288 ◽  
Author(s):  
Szilárd László
Keyword(s):  
Original Problem ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Dual Model ◽  
Vector Equilibrium Problems ◽  
Dual Approach ◽  
Topological Vector Spaces ◽  
Primal Dual ◽  
Vector Equilibrium ◽  
Weak Vector

AbstractIn this paper we provide some new sufficient conditions that ensure the existence of the solution of a weak vector equilibrium problem in Hausdorff topological vector spaces ordered by a cone. Further, we introduce a dual problem and we provide conditions that assure the solution set of the original problem and its dual coincide. We show that many known problems from the literature can be treated in our primal-dual model. We provide several coercivity conditions in order to obtain the existence of the solution of the primal-dual problems without compactness assumption. We apply the obtained results to perturbed vector equilibrium problems.

scholarly journals On the convexity of the solution set of symmetric vector equilibrium problems

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2097-2105 ◽  
Author(s):  
A.P. Farajzadeh
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Vector Equilibrium Problem ◽  
Solution Set ◽  
Vector Spaces ◽  
Vector Equilibrium Problems ◽  
Topological Vector Spaces ◽  
Vector Equilibrium

In this paper, without assumption of monotonicity and boundedness, we study existence results for a solution and the convexity of the solution set to the symmetric vector equilibrium problem for setvalued mappings in the setting of topological vector spaces. Our results improve the corresponding results in [9, 18, 19, 22, 28, 33, 36, 37].

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