eprintid: 4196
rev_number: 20
eprint_status: archive
userid: 351
dir: disk0/00/00/41/96
datestamp: 2016-01-15 02:04:46
lastmod: 2021-08-27 17:14:57
status_changed: 2016-01-15 02:04:46
type: monograph
metadata_visibility: show
item_issues_count: 2
creators_name: Kiwiel, K.
title: A Bundle of Method for Minimizing a Sum of Convex Functions with Smooth Weights
ispublished: pub
internal_subjects: iis_frc
internal_subjects: iis_met
internal_subjects: iis_mod
divisions: prog_opt
abstract: 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.
date: 1994-03
date_type: published
publisher: WP-94-013
iiasapubid: WP-94-013
price: 10
full_text_status: public
monograph_type: working_paper
place_of_pub: IIASA, Laxenburg, Austria
pages: 10
coversheets_dirty: FALSE
fp7_type: info:eu-repo/semantics/book
citation:   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     
document_url: https://pure.iiasa.ac.at/id/eprint/4196/1/WP-94-013.pdf