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 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.

scholarly journals Existence Results for Generalized Vector Equilibrium Problems with Multivalued Mappings via KKM Theory

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
A. P. Farajzadeh ◽  
A. Amini-Harandi ◽  
D. O'Regan
Keyword(s):  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Vector Equilibrium Problems ◽  
Solution Sets ◽  
Topological Vector Spaces ◽  
Set Valued Mapping ◽  
Generalized Vector Equilibrium Problems ◽  
Vector Equilibrium

We first define upper sign continuity for a set-valued mapping and then we consider two types of generalized vector equilibrium problems in topological vector spaces and provide sufficient conditions under which the solution sets are nonempty and compact. Finally, we give an application of our main results. The paper generalizes and improves results obtained by Fang and Huang in (2005).

scholarly journals Optimality Conditions for Vector Equilibrium Problems on Hadamard Manifolds

2019 ◽  
Author(s):  
Gabriel Ruiz-Garzón ◽  
Maria B. Donato ◽  
Rafaela Osuna-Gómez ◽  
Monica Milasi
Keyword(s):  
Optimality Conditions ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Vector Optimization Problem ◽  
Hadamard Manifolds ◽  
Vector Equilibrium Problems ◽  
Topological Vector Spaces ◽  
Weakly Efficient Solutions ◽  
Vector Equilibrium

The aim of this paper is to obtain Karush-Kuhn-Tucker optimality conditions for weakly efficient solutions to vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient solutions to the constrained vector optimization problem are presented. As well as some examples. The results presented in this paper generalize results obtained by Gong (2008) and Wei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces and real Banach spaces to Hadamard manifolds, respectively.

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.

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.

scholarly journals Traffic Network Equilibrium Problems with Capacity Constraints of Arcs and Linear Scalarization Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
X. Q. Tian ◽  
Y. D. Xu
Keyword(s):  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Capacity Constraints ◽  
Network Equilibrium ◽  
Traffic Network ◽  
Equilibrium Flow ◽  
Traffic Network Equilibrium ◽  
Vector Equilibrium ◽  
Network Equilibrium Problems ◽  
Weak Vector

Traffic network equilibrium problems with capacity constraints of arcs are studied. A (weak) vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of Lin (2010), and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a (weak) vector equilibrium flow to be a parametric equilibrium flow are derived. Relationships between a parametric equilibrium flow and a solution of a scalar variational inequality problem are also discussed. Some examples are given to illustrate our results.

scholarly journals GENERALIZED IMPLICIT INCLUSION PROBLEMS ON NONCOMPACT SETS WITH APPLICATIONS

2011 ◽  
Vol 84 (2) ◽  
pp. 261-279
Author(s):  
SAN-HUA WANG ◽  
NAN-JING HUANG
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Existence Results ◽  
Vector Spaces ◽  
Vector Equilibrium Problems ◽  
Inclusion Problems ◽  
Topological Vector Spaces ◽  
Vector Equilibrium

AbstractIn this paper, a class of generalized implicit inclusion problems is introduced, which can be regarded as a generalization of variational inequality problems, equilibrium problems, optimization problems and inclusion problems. Some existence results of solutions for such problems are obtained on noncompact subsets of Hausdorff topological vector spaces using the famous FKKM theorem. As applications, some existence results for vector equilibrium problems and vector variational inequalities on noncompact sets of Hausdorff topological vector spaces are given.

Sign in / Sign up

Export Citation Format

Share Document