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Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

Chowdhury, Mohammad (1998)

Serdica Mathematical Journal

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.Existence theorems of generalized variational inequalities and generalized complementarity problems are obtained in topological vector spaces for demi operators which are upper hemicontinuous along line segments in a convex set X. Fixed point theorems are also given in Hilbert spaces for set-valued operators T which are upper hemicontinuous along line segments in X such...

Inégalités variationnelles non convexes

Messaoud Bounkhel, Djalel Bounkhel (2005)

ESAIM: Control, Optimisation and Calculus of Variations

Dans cet article nous proposons différents algorithmes pour résoudre une nouvelle classe de problèmes variationels non convexes. Cette classe généralise plusieurs types d’inégalités variationnelles (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) du cas convexe au cas non convexe. La sensibilité de cette classe de problèmes variationnels non convexes a été aussi étudiée.

Inertial forward-backward splitting method in Banach spaces with application to compressed sensing

Prasit Cholamjiak, Yekini Shehu (2019)

Applications of Mathematics

We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the few available inertial-type methods for zeros of the sum of accretive operators in Banach spaces.

Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities

Martin Väth (2014)

Mathematica Bohemica

We consider a reaction-diffusion system of activator-inhibitor type which is subject to Turing's diffusion-driven instability. It is shown that unilateral obstacles of various type for the inhibitor, modeled by variational inequalities, lead to instability of the trivial solution in a parameter domain where it would be stable otherwise. The result is based on a previous joint work with I.-S. Kim, but a refinement of the underlying theoretical tool is developed. Moreover, a different regime of parameters...

Interior proximal method for variational inequalities on non-polyhedral sets

Alexander Kaplan, Rainer Tichatschke (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Interior proximal methods for variational inequalities are, in fact, designed to handle problems on polyhedral convex sets or balls, only. Using a slightly modified concept of Bregman functions, we suggest an interior proximal method for solving variational inequalities (with maximal monotone operators) on convex, in general non-polyhedral sets, including in particular the case in which the set is described by a system of linear as well as strictly convex constraints. The convergence analysis of...

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