A new interior point method for the variational inequality problem

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:36155

Iusem, A; Burachik, R

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 needs 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 raise to explicit iteration formulae, up to the determination of two scalar stepsizes, which can be found through finite search procedures.

• OSTI ID: 36155
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
LINEAR PROGRAMMING
OPTIMIZATION
VARIATIONAL METHODS