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Globally convergent block-coordinate techniques for unconstrained optimization. (English) Zbl 0940.65070
A class of globally convergent block-coordinate methods for minimizing a continuously differentiable function is defined. First, sufficient convergence criteria are expressed in terms of conditions on the elementary operations performed on each block component and suitable (sequential or parallel) connection rules are studied. Then inexact line searches are described that yield both a constructive device for proving convergence and effective computational tools. Combining these, the convergence analysis of the nonlinear Gauss-Seidel method for minimization is performed. In the case of a two-block decomposition, the Gauss-Seidel method is proved to globally converge towards stationary points, under mild assumptions that do not include convexity or uniqueness. Also the computational aspects and potential advantages of the new methods are discussed with the application to a learning problem in a radial basis function neural network.

MSC:
65K05 Numerical mathematical programming methods
68T05 Learning and adaptive systems in artificial intelligence
90C26 Nonconvex programming, global optimization
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