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On the convergence of the block nonlinear Gauss-Seidel method under convex constraints. (English) Zbl 0955.90128
Summary: 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 modification of the method and we state convergence results without any convexity assumption on the objective function.

90C30Nonlinear programming
49M27Decomposition methods in calculus of variations
65K05Mathematical programming (numerical methods)
Full Text: DOI
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