Vector quasi-equilibrium problems: separation, saddle points and error bounds for the solution set

Authors:
S. -M. Guu;J. Li
Affiliations:
Graduate Institute of Business and Management, College of Management, Chang-Gung University, Kwei-Shan, Taoyuan Hsien, Taiwan 333;College of Mathematics and Information, China West Normal University, Nanchong, China 637009
Venue:
Journal of Global Optimization
Year:
2014

Citing 11
Cited 0

Semidifferentiable functions and necessary optimality conditions

Journal of Optimization Theory and Applications
Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems

Mathematical Programming: Series A and B
Partially finite convex programming, part I: quasi relative interiors and duality theory

Mathematical Programming: Series A and B
Quasi interiors, Lagrange multipliers, and Lp spectral estimation with lattice bounds

Journal of Optimization Theory and Applications
Error bounds in mathematical programming

Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
The System of Vector Quasi-Equilibrium Problems with Applications

Journal of Global Optimization
Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems

Journal of Global Optimization
Regularity Conditions via Quasi-Relative Interior in Convex Programming

SIAM Journal on Optimization
Separation of sets and Wolfe duality

Journal of Global Optimization
Remarks on infinite dimensional duality

Journal of Global Optimization
On the image space analysis for vector quasi-equilibrium problems with a variable ordering relation

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we employ the image space analysis (for short, ISA) to investigate vector quasi-equilibrium problems (for short, VQEPs) with a variable ordering relation, the constrained condition of which also consists of a variable ordering relation. The quasi relatively weak VQEP (for short, qr-weak VQEP) are defined by introducing the notion of the quasi relative interior. Linear separation for VQEP (res., qr-weak VQEP) is characterized by utilizing the quasi interior of a regularization of the image and the saddle points of generalized Lagrangian functions. Lagrangian type optimality conditions for VQEP (res., qr-weak VQEP) are then presented. Gap functions for VQEP (res., qr-weak VQEP) are also provided and moreover, it is shown that an error bound holds for the solution set of VQEP (res., qr-weak VQEP) with respect to the gap function under strong monotonicity.