Global minimization for generalized polynomial fractional program
type: Item
instance of: scholarly article
title: Global minimization for generalized polynomial fractional program
zbMATH Open document ID: 1407.90315
DOI: 10.1155/2014/567680
author: Xue-Ping Hou
author: Peiping Shen
author: Chunfeng Wang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper is concerned with an efficient global optimization algorithm for solving a kind of fractional program problem \((\text{P})\), whose objective and constraints functions are all defined as the sum of ratios generalized polynomial functions. The proposed algorithm is a combination of the branch-and-bound search and two reduction operations, based on an equivalent monotonic optimization problem of \((\text{P})\). The proposed reduction operations specially offer a possibility to cut away a large part of the currently investigated region in which the global optimal solution of \((\text{P})\) does not exist, which can be seen as an accelerating device for the solution algorithm of \((\text{P})\). Furthermore, numerical results show that the computational efficiency is improved by using these operations in the number of iterations and the overall execution time of the algorithm, compared with other methods. Additionally, the convergence of the algorithm is presented, and the computational issues that arise in implementing the algorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach for solving problem \((\text{P})\) provided that the number of variables is not too large.
Mathematics Subject Classification ID: 90C32
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 7016744
Wikidata QID: Q59066042
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/567680
OpenAlex ID: W2090028595
cites work: Solving long-term financial planning problems via global optimization
cites work: Q4352213
cites work: Q4368736
cites work: BOND PORTFOLIO OPTIMIZATION PROBLEMS AND THEIR APPLICATIONS TO INDEX TRACKING : A PARTIAL OPTIMIZATION APPROACH
cites work: Effectiveness of a geometric programming algorithm for optimization of machining economics models
cites work: An efficient algorithm for solving convex-convex quadratic fractional programs
cites work: A simplicial branch and bound duality-bounds algorithm for the linear sum-of-ratios problem
cites work: Solving sum of quadratic ratios fractional programs via monotonic function
cites work: Global optimization of generalized linear fractional programming with nonlinear constraints
cites work: An efficient algorithm for globally minimizing sum of quadratic ratios problem with nonconvex quadratic constraints
cites work: Decomposition branch-and-bound based algorithm for linear programs with additional multiplicative constraints
cites work: Global optimization of multiplicative programs
cites work: Finite algorithm for generalized linear multiplicative programming
cites work: A robust algorithm for generalized geometric programming
cites work: A global optimization using linear relaxation for generalized geometric programming
cites work: Global optimization of generalized geometric programming
cites work: Global optimization of signomial geometric programming using linear relaxation.
cites work: \(NP\)-hardness of linear multiplicative programming and related problems
cites work: A branch-and-bound algorithm for maximizing the sum of several linear ratios
cites work: Global optimization of nonlinear sum of ratios problem
cites work: Global optimization for the sum of generalized polynomial fractional functions
cites work: Global optimization algorithm for sum of generalized polynomial ratios problem
cites work: Global optimization for a class of fractional programming problems
cites work: Monotonic Optimization: Branch and Cut Methods
description: scientific article; zbMATH DE number 7016744