On the convergence of the block nonlinear Gauss-Seidel method under convex constraints

We give new convergence results fur the block Gauss-Seidel method for problems where the feasible set is the Cartesian product of m closed convex sets, under the assumption that the sequence generated by the method has limit points. We show that the method is globally convergent for m = 2 and that for in > 2 convergence can be established both when the objective function f is componentwise strictly quasiconvex with respect to m - 2 components and when f is pseudoconvex. Finally, we consider a proximal point modification of the method and we state convergence results without any convexity assumption on the objective function. (C) 2000 Elsevier Science B.V. All rights reserved.