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Gap functions for quasi-variational inequalities via duality. [PDF]

J Inequal Appl, 2018
This paper deals with an application of duality theory in optimization to the construction of gap functions for quasi-variational inequalities. The same approach was investigated for variational inequalities and equilibrium problems in (Pac. J. Optim.
Altangerel L.
europepmc   +2 more sources

The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces

European Journal of Operational Research, 2020
Tseng's forward-backward-forward algorithm is a valuable alternative for Korpelevich's extragradient method when solving variational inequalities over a convex and closed set governed by monotone and Lipschitz continuous operators, as it requires in ...
Bot, Radu Ioan, Csetnek, Ernö Robert, Vuong, Phan Tu   +2 more
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Novel Algorithms for Solving a System of Absolute Value Variational Inequalities

Journal of Function Spaces, 2022
The goal of this paper is to study a new system of a class of variational inequalities termed as absolute value variational inequalities. Absolute value variational inequalities present a rational, pragmatic, and novel framework for investigating a wide ...
Safeera Batool, Muhammad Aslam Noor, Riaz Ahmad, Ilyas Khan, Mulugeta Andualem   +4 more
doaj   +1 more source

Inexact Model: A Framework for Optimization and Variational Inequalities [PDF]

, 2020
In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities.
Agafonov, Artem, Dvinskikh, Darina, Dvurechensky, Pavel, Gasnikov, Alexander, Kroshnin, Alexey, Pasechnyuk, Dmitry, Piskunova, Victorya, Stonyakin, Fedor, Tyurin, Alexander   +8 more
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Auxiliary Principle for Generalized Strongly Nonlinear Mixed Variational-Like Inequalities

Journal of Inequalities and Applications, 2009
We introduce and study a class of generalized strongly nonlinear mixed variational-like inequalities, which includes several classes of variational inequalities and variational-like inequalities as special cases.
Zeqing Liu, Lin Chen, Jeong Sheok Ume, Shin Min Kang   +3 more
doaj   +2 more sources

Variational Inequalities in Critical-State Problems [PDF]

, 2004
Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and elastoplastic ...
Aronsson, Badía, Bak, Barrett, Bean, Bossavit, Bouchaud, Brandt, de Gennes, Duvaut, Ekeland, Evans, Evans, Glowinski, Han, Jackson, Kim, Leonid Prigozhin, Prager, Prigozhin, Prigozhin, Prigozhin, Prigozhin, Prigozhin, Prigozhin, Prigozhin, Puhl, Shuster, Temam, Yin   +29 more
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The Solvability of a Class of General Nonlinear Implicit Variational Inequalities Based on Perturbed Three-Step Iterative Processes with Errors

Fixed Point Theory and Applications, 2008
We introduce and study a new class of general nonlinear implicit variational inequalities, which includes several classes of variational inequalities and variational inclusions as special cases.
Jeong Sheok Ume, Shin Min Kang, Zeqing Liu   +2 more
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Some Aspects of Extended General Variational Inequalities

Abstract and Applied Analysis, 2012
Noor (“Extended general variational inequalities,” 2009, “Auxiliary principle technique for extended general variational inequalities,” 2008, “Sensitivity analysis of extended general variational inequalities,” 2009, “Projection iterative methods for ...
Muhammad Aslam Noor
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Vector Optimization Problems and Generalized Vector Variational-Like Inequalities [PDF]

Sahand Communications in Mathematical Analysis, 2020
In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak ...
Ildar Sadeqi, Somayeh Nadi
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Existence of Solutions for η-Generalized Vector Variational-Like Inequalities

Journal of Inequalities and Applications, 2010
We introduce and study a class of η-generalized vector variational-like inequalities and a class of η-generalized strong vector variational-like inequalities in the setting of Hausdorff topological vector spaces.
Xi Li, Jong Kyu Kim, Nan-Jing Huang
doaj   +1 more source