Interior projection-like methods for monotone variational inequalities

摘要: We propose new interior projection type methods for solving monotone variational inequalities. The can be viewed as a natural extension of the extragradient and hyperplane algorithms, are based on using non Euclidean projection-like maps. prove global convergence results establish rate estimates. maps given by analytical formulas standard constraints such box, simplex, conic constraints, generate trajectories. then demonstrate that within an appropriate primal-dual inequality framework, proposed algorithms applied to general convex resulting in which at each iteration entail only explicit do not require solution any optimization problem. As consequence, easy implement, with low computational cost, naturally lead decomposition schemes problems separable structure. This is illustrated through examples programming, convex-concave saddle point semidefinite programming.