ALTERNATING PROJECTION-PROXIMAL METHODS FOR CONVEX-PROGRAMMING AND VARIATIONAL-INEQUALITIES

We consider a mixed problem composed in part of finding a zero of a ma ximal monotone operator and in part of solving a monotone variational inequality problem. We propose a solution method for this problem that alternates between a proximal step (for the maximal monotone operator part) and a projection-type step (for the monotone variational inequa lity part) and analyze its convergence and rate of convergence. This m ethod extends a decomposition method of Chen and Teboulle [Math. Progr amming, 64 (1994), pp. 81-101] for convex programming and yields, as a by-product, new decomposition methods.