relation: https://pure.iiasa.ac.at/id/eprint/4196/
title: A Bundle of Method for Minimizing a Sum of Convex Functions with Smooth Weights
creator: Kiwiel, K.
description: 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.
publisher: WP-94-013
date: 1994-03
type: Monograph
type: NonPeerReviewed
format: text
language: en
identifier: https://pure.iiasa.ac.at/id/eprint/4196/1/WP-94-013.pdf
identifier:   Kiwiel, K.  (1994).  A Bundle of Method for Minimizing a Sum of Convex Functions with Smooth Weights.   IIASA Working Paper. IIASA, Laxenburg, Austria: WP-94-013