A CHARACTERIZATION OF THE SET OF FIXED-POINTS OF SOME SMOOTHED OPERATORS

We characterize the set F of fixed points of an operator T(x) = SQ(x), where S is a positive definite, symmetric, and stochastic matrix and Q is a convex combination of orthogonal projections onto closed convex sets. We show that F is the set of minimizers of a convex function: the sum of a weighted average of the squares of the distances to the convex sets and a nonnegative quadratic related to the matrix S.1771

CONVERGENCE PROPERTIES OF ITERATIVE METHODS FOR SYMMETRICAL POSITIVE SEMIDEFINITE LINEAR COMPLEMENTARITY-PROBLEMS

We consider iterative methods using splittings for solving symmetric positive semidefinite linear complementarily problems. We prove strong convergence, i.e., convergence of the whole sequence, for these types of methods with the only hypothesis of existence of a solution. To do this we introduce dual methods for solving a dual quadratic programming problem and we prove linear convergence of such methods.18231733

ON THE CONVERGENCE OF SOR-TYPE AND JOR-TYPE METHODS FOR CONVEX LINEAR COMPLEMENTARITY-PROBLEMS

We consider SOR- and JOR-type iterative methods for solving linear complementarity problems. If the solution set is not discrete, weak-convergence proofs are usually obtained for these methods; i.e., every accumulation point of the generated sequence is a solution. We prove that, for the convex case, the whole sequence converges, and if the limit point is nondegenerate, convergence is linear.15460161