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We give new convergence results for 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 m ¿ 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 modiÿcation of the method and we state convergence results without any convexity assumption on the objective function.

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