scholarly journals Hybrid Approximate Proximal Method with Auxiliary Variational Inequality for Vector Optimization

2010 ◽  
Vol 146 (2) ◽  
pp. 267-303 ◽  
Author(s):  
L. C. Ceng ◽  
B. S. Mordukhovich ◽  
J. C. Yao
Keyword(s):  
Variational Inequality ◽  
Vector Optimization ◽  
Proximal Method

An interior proximal method in vector optimization

2011 ◽  
Vol 214 (3) ◽  
pp. 485-492 ◽  
Author(s):  
Kely D.V. Villacorta ◽  
P. Roberto Oliveira
Keyword(s):  
Vector Optimization ◽  
Proximal Method

scholarly journals PARALLEL EXTRAGRADIENT-PROXIMAL METHODS FOR SPLIT EQUILIBRIUM PROBLEMS

2016 ◽  
Vol 21 (4) ◽  
pp. 478-501 ◽  
Author(s):  
Dang Van Hieu
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Projection Method ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Proximal Methods ◽  
Proximal Method ◽  
Weak And Strong Convergence ◽  
Split Variational Inequality

In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. We also present an application to split variational inequality problems and a numerical example to illustrate the convergence of the proposed algorithms.

scholarly journals ALGORITHM FOR VARIATIONAL INEQUALITY PROBLEM OVER THE SET OF SOLUTIONS THE EQUILIBRIUM PROBLEMS

2020 ◽  
pp. 18-30
Author(s):  
Ya. I. Vedel ◽  
S. V. Denisov ◽  
V. V. Semenov
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problems ◽  
Variational Inequality Problem ◽  
Proximal Method ◽  
Iterative Regularization ◽  
Inequality Problem ◽  
Lipschitz Continuous ◽  
Convergence Of Sequences ◽  
Continuous Operators ◽  
Monotone Bifunctions

In this paper, we consider bilevel problem: variational inequality problem over the set of solutions the equilibrium problems. To solve this problem, an iterative algorithm is proposed that combines the ideas of a two-stage proximal method and iterative regularization. For monotone bifunctions of Lipschitz type and strongly monotone Lipschitz continuous operators, the theorem on strong convergence of sequences generated by the algorithm is proved.

scholarly journals Interval-Valued Vector Optimization Problems Involving Generalized Approximate Convexity

2020 ◽  
Author(s):  
Mohsine Jennane ◽  
Lhoussain El Fadil ◽  
El Mostafa Kalmoun
Keyword(s):  
Variational Inequality ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Sufficient Optimality Conditions ◽  
Approximate Convexity ◽  
Study Interval ◽  
Necessary And Sufficient ◽  
Interval Valued

Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexity, we establish necessary and sufficient optimality conditions for local strong quasi and approximate $LU$-efficient solutions to nonsmooth optimization problems with interval-valued multiobjective functions.

Sign in / Sign up

Export Citation Format

Share Document