inverse strongly-monotone operator

A von Neumann Alternating Method for Finding Common Solutions to Variational Inequalities

Published: 2012/02/03

Complementarity and Variational Inequalities, Nonlinear Optimization alternating method, averaged operator, fixed point, hilbert space, inverse strongly-monotone operator, metric projection, nonexpansive operator, resolvent, variational inequality

Modifying von Neumann’s alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space. CitationNonlinear Analysis Series A: Theory, Methods & Applications, … Read more

Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces

Published: 2005/01/16, Updated: 2005/01/18

Dan Butnariu

Elena Resmerita

Convex and Nonsmooth Optimization bregman distance, bregman projection, e-space, essential strict convexity, inverse monotone operator, inverse strongly-monotone operator, mosco convergence, relative projection, total convexity, uniform convexity

The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity … Read more