Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions

- Chen, Yi, Gao, David

Title
Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions
Creator
Chen, Yi; Gao, David
Date
2016
Type
Text; Journal article
Identifier
http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100457
Identifier
vital:10548
Identifier
https://doi.org/10.1007/s10898-014-0244-5
Identifier
ISSN:0925-5001
Abstract
This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of 4th-order polynomial and a log-sum-exp function. Such a problem arises extensively in engineering and sciences. Based on the canonical duality–triality theory, this nonconvex problem is transformed to an equivalent dual problem, which can be solved easily under certain conditions. We proved that both global minimizer and the biggest local extrema of the primal problem can be obtained analytically from the canonical dual solutions. As two special cases, a quartic polynomial minimization and a minimax problem are discussed. Existence conditions are derived, which can be used to classify easy and relative hard instances. Applications are illustrated by several nonconvex and nonsmooth examples. © 2014, Springer Science+Business Media New York.
Publisher
Springer New York LLC
Relation
Journal of Global Optimization Vol. 64, no. 3 (2016), p. 417-431
Rights
Copyright © Springer Science+Business Media New York 2014
Rights
Open Access
Rights
This metadata is freely available under a CCO license
Subject
0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0802 Computation Theory and Mathematics; Canonical duality theory; Double-well function; Global optimization; Log-sum-exp function; Minimax problems; Polynomial minimisation
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