TY  - RPRT
CY  - IIASA, Laxenburg, Austria
ID  - iiasa4196
UR  - https://pure.iiasa.ac.at/id/eprint/4196/
A1  - Kiwiel, K.
Y1  - 1994/03//
N2  - 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.
PB  - WP-94-013
M1  - working_paper
TI  - A Bundle of Method for Minimizing a Sum of Convex Functions with Smooth Weights
AV  - public
EP  - 10
ER  -