A Bundle of Method for Minimizing a Sum of Convex Functions with Smooth Weights

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/3975 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/3975 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/3975 archive 351 disk0/00/00/41/96 2016-01-15 02:04:46 2021-08-27 17:14:57 2016-01-15 02:04:46 monograph show 2 Kiwiel K. A Bundle of Method for Minimizing a Sum of Convex Functions with Smooth Weights pub iis_frc iis_met iis_mod prog_opt We give a bundle method for minimizing a (possibly nondifferentiable and nonconvex) function h(z) = sum_{i=1}^m p_i(x) f_i(x) over a closed convex set in R^n, where p_i are nonnegative and smooth and f_i are finite-valued convex. Such functions arise in certain stochastic programming problems and scenario analysis. The method finds search directions via quadratic programming, using a polyhedral model of h that involves current linearizations of p_i and polyhedral models of f_i based on their accumulated subgradients. We show that the method is globally convergent to stationary points of h. The method exploits the structure of h and hence seems more promising than general-purpose bundle methods for nonconvex minimization. 1994-03 published WP-94-013 WP-94-013 10 public working_paper IIASA, Laxenburg, Austria 10 FALSE info:eu-repo/semantics/book