A projection algorithm for non-monotone variational inequalities

2016/09/30 by Burachik, Regina S., Millán, R. Díaz
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1609.09569

Abstract

We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the problem is only assumed to be continuous in the point-to-set sense, i.e., inner- and outer-semicontinuous. Additionally, we assume non-emptiness of the so-called dual solution set. We prove that the whole sequence of iterates converges to a solution of the variational inequality. Moreover, we provide numerical experiments illustrating the behavior of our iterates. Through several examples, we provide a comparison with a recent similar algorithm.

Related

• Beyond Monotone Variational Inequalities: Solution Methods and Iteration Complexities
• A new version of projection method for variational inequalities problem with nonlinear constraints
• Convergence analysis for pseudo-monotone variational inequality problem involving projections onto a moving ball
• A New Iterative Projection Method for Approximating Fixed Point Problems and Variational Inequality Problems
• A Relaxed-Projection Splitting Algorithm for Variational Inequalities in Hilbert Spaces