An effective linear approximation method for separable programming problems
type: Item
instance of: scholarly article
title: An effective linear approximation method for separable programming problems
zbMATH Open document ID: 1192.65077
author: Chiahui Huang
published in: Applied Mathematics and Computation
publication date: 2009-11-13T00:00:00Z
review text: The author introduces a piecewise linearization method to solve separable programs. Here, instead of the usual \(m\) binary variables, \(\lceil \log_2(m-1) \rceil\) variables are used to linearize the concave functions. This is of interest for decreasing the runtime of the optimization procedure for big problems with large \(m\). Examples are given that are solved numerically to accentuate the improvements achieved with the method.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 5632596
zbMATH Keywords: separable programming
zbMATH Keywords: piecewise linearization
zbMATH Keywords: numerical examples
reviewed by: M. D. Korzec
MaRDI profile type: Publication
full work available at URL: j.amc.2009.07.007
OpenAlex ID: W2017675572
cites work: A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design
cites work: Solving the uncapacitated network design problem by a Lagrangean heuristic and branch-and-bound
cites work: Flow pack facets of the single node fixed-charge flow polytope
cites work: A branch‐and‐cut algorithm for the single‐commodity, uncapacitated, fixed‐charge network flow problem
cites work: Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
cites work: Q3134873
cites work: A practical guide to splines.
cites work: Q4331736
cites work: Deterministic global optimization. Theory, methods and applications
cites work: A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique
cites work: Exploiting special structures in constructing a hierarchy of relaxations for \(0-1\) mixed integer problems
cites work: Objective function approximations in mathematical programming
cites work: Optimal objective function approximation for separable convex quadratic programming
cites work: The facility location problem with general cost functions
cites work: Global minimization of large-scale constrained concave quadratic problems by separable programming
cites work: Error Analysis for Convex Separable Programs: The Piecewise Linear Approximation and The Bounds on The Optimal Objective Value
cites work: A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems
cites work: Practical piecewise-linear approximation for monotropic optimization
cites work: Approximating separable nonlinear functions via mixed zero-one programs
cites work: An algorithm for approximating piecewise linear concave functions from sample gradients
cites work: Discharge allocation for hydro-electric generating stations
cites work: Q4068464
DOI: 10.1016/J.AMC.2009.07.007
description: scientific article; zbMATH DE number 5632596