scholarly journals Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Wei-bing Zhang ◽  
Nan-jing Huang ◽  
Donal O’Regan
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Quasi Equilibrium ◽  
Well Posedness ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalarization Function

We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem.

scholarly journals Constrained Weak Nash-Type Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
W. C. Shuai ◽  
K. L. Xiang ◽  
W. Y. Zhang
Keyword(s):  
Existence Theorem ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalarization Function ◽  
Payoff Functions

A constrained weak Nash-type equilibrium problem with multivalued payoff functions is introduced. By virtue of a nonlinear scalarization function, some existence results are established. The results extend the corresponding one of Fu (2003). In particular, if the payoff functions are singlevalued, our existence theorem extends the main results of Fu (2003) by relaxing the assumption of convexity.

scholarly journals LP Well-Posedness for Bilevel Vector Equilibrium and Optimization Problems with Equilibrium Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Phan Quoc Khanh ◽  
Somyot Plubtieng ◽  
Kamonrat Sombut
Keyword(s):  
Equilibrium Problems ◽  
Optimization Problems ◽  
Well Posedness ◽  
Equilibrium Constraints ◽  
Vector Equilibrium Problems ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Measures Of Noncompactness ◽  
Scalarization Function ◽  
Vector Equilibrium

The purpose of this paper is introduce several types of Levitin-Polyak well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints. Base on criterion and characterizations for these types of Levitin-Polyak well-posedness we argue on diameters and Kuratowski’s, Hausdorff’s, or Istrǎtescus measures of noncompactness of approximate solution sets under suitable conditions, and we prove the Levitin-Polyak well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints. Obtain a gap function for bilevel vector equilibrium problems with equilibrium constraints using the nonlinear scalarization function and consider relations between these types of LP well-posedness for bilevel vector optimization problems with equilibrium constraints and these types of Levitin-Polyak well-posedness for bilevel vector equilibrium problems with equilibrium constraints under suitable conditions; we prove the Levitin-Polyak well-posedness for bilevel equilibrium and optimization problems with equilibrium constraints.

scholarly journals Existence and Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Kaihong Wang ◽  
Wenyan Zhang ◽  
Min Fang
Keyword(s):  
Existence Result ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Solution Set ◽  
Quasi Equilibrium ◽  
Well Posedness

An existence result for the solution set of symmetric vector quasi-equilibrium problems that allows for discontinuities is obtained. Moreover, sufficient conditions for the generalized Levitin-Polyak well-posedness of symmetric vector quasi-equilibrium problems are established.

Well-Posedness for Parametric Generalized Strong Vector Quasi-Equilibrium Problem

2014 ◽  
Vol 556-562 ◽  
pp. 4093-4096
Author(s):  
Ya Li Zhao ◽  
Lin Zhu
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Quasi Equilibrium ◽  
Well Posedness

In this paper, well-posedness for parametric generalized strong vector quasi-equilibrium problems is studied. The corresponding concept of well-posedness in the generalized sense is also investigated for the parametric generalized strong vector quasi-equilibrium problem. Under some suitable conditions, we establish some characterizations of well-posedness for the parametric generalized strong vector quasi-equilibrium problem.

scholarly journals Scalarization and well-posedness for set optimization using coradiant sets

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3457-3471
Author(s):  
Bin Yao ◽  
Sheng Li
Keyword(s):  
Optimization Problem ◽  
Set Optimization ◽  
Well Posedness ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalar Optimization ◽  
Set Optimization Problem ◽  
Order Relations ◽  
Scalarization Function

The aim of this paper is to study scalarization and well-posedness for a set-valued optimization problem with order relations induced by a coradiant set. We introduce the notions of the set criterion solution for this problem and obtain some characterizations for these solutions by means of nonlinear scalarization. The scalarization function is a generalization of the scalarization function introduced by Khoshkhabar-amiranloo and Khorram. Moveover, we define the pointwise notions of LP well-posedness, strong DH-well-posedness and strongly B-well-posedness for the set optimization problem and characterize these properties through some scalar optimization problem based on the generalized nonlinear scalarization function respectively.

scholarly journals Existence of Solutions for Generalized Vector Quasi-Equilibrium Problems by Scalarization Method with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
De-ning Qu ◽  
Cao-zong Cheng
Keyword(s):  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Inclusion Problem ◽  
Quasi Equilibrium ◽  
Nonlinear Scalarization ◽  
Topological Vector Spaces ◽  
Variational Inclusion Problem ◽  
Scalarization Method ◽  
Scalarization Function ◽  
Locally Convex

The aim of this paper is to study generalized vector quasi-equilibrium problems (GVQEPs) by scalarization method in locally convex topological vector spaces. A general nonlinear scalarization function for set-valued mappings is introduced, its main properties are established, and some results on the existence of solutions of the GVQEPs are shown by utilizing the introduced scalarization function. Finally, a vector variational inclusion problem is discussed as an application of the results of GVQEPs.

Levitin-Polyak well-posedness for parametric quasivariational inclusion and disclusion problems

2018 ◽  
Vol 34 (3) ◽  
pp. 295-303
Author(s):  
PANATDA BOONMAN ◽  
◽  
RABIAN WANGKEEREE ◽  
Keyword(s):  
Equilibrium Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Well Posedness ◽  
Quasiequilibrium Problems ◽  
Necessary And Sufficient

In this paper, we aim to suggest the new concept of Levitin-Polyak (for short, LP) well-posedness for the parametric quasivariational inclusion and disclusion problems (for short, (QVIP) (resp. (QVDP))). Necessary and sufficient conditions for LP well-posedness of these problems are proved. As applications, we obtained immediately some results of LP well-posedness for the quasiequilibrium problems and for a scalar equilibrium problem.

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.

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