An interior point method with Bregman functions for the variational inequality problem with paramonotone operators

An interior point method with Bregman functions for the variational inequality problem with paramonotone operators

0.00 Avg rating0 Votes
Article ID: iaor19992588
Country: Netherlands
Volume: 81
Issue: 3
Start Page Number: 373
End Page Number: 400
Publication Date: May 1998
Journal: Mathematical Programming
Authors: , ,
Keywords: interior point methods
Abstract:

We present an algorithm for the variational inequality problem on convex sets with nonempty interior. The use of Bregman functions whose zone is the convex set allows for the generation of a sequence contained in the interior, without taking explicitly into account the constraints which define the convex set. We establish full convergence to a solution with minimal conditions upon the monotone operator F, weaker than strong monotonicity or Lipschitz continuity, for instance, and including cases where the solution need not be unique. We apply our algorithm to several relevant classes of convex sets, including orthants, boxes, polyhedra and balls, for which Bregman functions are presented which give rise to explicit iteration formulae, up to the determination of two scalar stepsizes, which can be found through finite search procedures.

Reviews

Required fields are marked *. Your email address will not be published.