scholarly journals Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems

1992 ◽  
Vol 53 (1-3) ◽  
pp. 99-110 ◽  
Author(s):  
Masao Fukushima
Keyword(s):  
Variational Inequality ◽  
Optimization Problems ◽  
Variational Inequality Problems ◽  
Descent Methods

scholarly journals Vector and Ordered Variational Inequalities and Applications to Order-Optimization Problems on Banach Lattices

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Linsen Xie ◽  
Jinlu Li ◽  
Wenshan Yang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Fixed Point Theorems ◽  
Optimization Problems ◽  
Banach Lattices ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Real Vector ◽  
Finite Dimensional

We investigate the connections between vector variational inequalities and ordered variational inequalities in finite dimensional real vector spaces. We also use some fixed point theorems to prove the solvability of ordered variational inequality problems and their application to some order-optimization problems on the Banach lattices.

scholarly journals Variational-like inequalities for n-dimensional fuzzy-vector-valued functions and fuzzy optimization

2019 ◽  
Vol 17 (1) ◽  
pp. 627-645
Author(s):  
Ting Xie ◽  
Zengtai Gong
Keyword(s):  
Variational Inequality ◽  
Fuzzy Number ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Decomposition Theorem ◽  
Variational Inequality Problems ◽  
Multiobjective Optimization Problems ◽  
Vector Valued Functions ◽  
The Relationship ◽  
Vector Valued

Abstract The existing results on the variational inequality problems for fuzzy mappings and their applications were based on Zadeh’s decomposition theorem and were formally characterized by the precise sets which are the fuzzy mappings’ cut sets directly. That is, the existence of the fuzzy variational inequality problems in essence has not been solved. In this paper, the fuzzy variational-like inequality problems is incorporated into the framework of n-dimensional fuzzy number space by means of the new ordering of two n-dimensional fuzzy-number-valued functions we proposed [Fuzzy Sets and Systems 295 (2016) 19-36]. As a theoretical basis, the existence and the basic properties of the fuzzy variational inequality problems are discussed. Furthermore, the relationship between the variational-like inequality problems and the fuzzy optimization problems is discussed. Finally, we investigate the optimality conditions for the fuzzy multiobjective optimization problems.

scholarly journals Approximate-Karush-Kuhn-Tucker Conditions and Interval Valued Vector Variational Inequalities

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Vector Variational Inequality ◽  
Vector Variational Inequalities ◽  
Variational Inequality Problems ◽  
Objective Functions ◽  
Interval Valued

This Article deals with the Approximate Karush-Kuhn-Tucker (AKKT) optimality conditions for interval valued multiobjective function as a generalization of Karush-Kuhn-Tucker optimality conditions. Further, we establish relationship between vector variational inequality problems and multiobjective interval valued optimization problems under the assumption of LU−convex smooth and nonsmooth objective functions.

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