Abstract
We present a new variant of the block nonlinear Gauss-Seidel algorithm for solving convex minimization problems over polyhedral constraints. The method is based on coupling the recent logarithmic-quadratic proximal method introduced by the authors, with the coordinate descent strategie for problems with block structure. Our approach allows for eliminating the constraints, and removing the usual strict convexity assumption used in a Gauss-Seidel type algorithm. Thus, for each block the algorithm consists of solving an unconstrained convex problem, which can be solved efficiently via Newton type method, and leads to an attractive decomposition scheme. We prove under mild assumptions on the problems data, that all limit points of the sequence generated by the proposed algorithm are optimal solutions.
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© 1999 Springer-Verlag Berlin Heidelberg
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Auslender, A., Teboulle, M., Ben-Tiba, S. (1999). Coupling the Logarithmic-Quadratic Proximal Method and the Block Nonlinear Gauss-Seidel Algorithm for Linearly Constrained Convex Minimization. In: Théra, M., Tichatschke, R. (eds) Ill-posed Variational Problems and Regularization Techniques. Lecture Notes in Economics and Mathematical Systems, vol 477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45780-7_3
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DOI: https://doi.org/10.1007/978-3-642-45780-7_3
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