Vol. 3, No. 2, 2015
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ISSN: 2325-3444 (e-only)
ISSN: 2326-7186 (print)
Canonical duality theory and triality for solving general global optimization problems in complex systems

Daniel Morales-Silva and David Y. Gao

Vol. 3 (2015), No. 2, 139–161
DOI: 10.2140/memocs.2015.3.139
Abstract

General nonconvex optimization problems are studied by using the canonical duality-triality theory. The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. This theory can be used to find the global minimum and local extrema, which bridges a gap between global optimization and nonconvex mechanics. Detailed applications are illustrated by several examples.

Keywords
canonical duality, triality theory, nonlinear analysis, nonconvex optimization, complex systems
Mathematical Subject Classification 2010
Primary: 49N15, 90C26
Milestones
Received: 22 April 2013
Revised: 13 May 2014
Accepted: 29 July 2014
Published: 16 May 2015

Communicated by Martin Ostoja-Starzewski
Authors
Daniel Morales-Silva
School of Science
Information Technology and Engineering
Federation University
Mt. Helen VIC 3353
Australia
David Y. Gao
School of Science
Information Technology and Engineering
Federation University
Mt. Helen, VIC 3353
Australia		 Research School of Engineering
Australian National University
Canberra, ACT 0200
Australia