Abstract
This paper presents a descent method for minimizing a sum of possibly nonsmooth convex functions. Search directions are found by solving subproblems obtained by replacing all but one of the component functions with their polyhedral approximations and adding a quadratic term. The algorithm is globally convergent and terminates when the objective function happens to be polyhedral. It yields a new decomposition method for solving large-scale linear programs with dual block-angular structure.
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Communicated by D. Q. Mayne
Supported by Program CPBP 02.15.
The author thanks the two referees for their helpful suggestions.
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Kiwiel, K.C. Decomposition method of descent for minimizing the sum of convex nonsmooth functions. J Optim Theory Appl 52, 255–271 (1987). https://doi.org/10.1007/BF00941285
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DOI: https://doi.org/10.1007/BF00941285