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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
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 49N15, 90C26
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Milestones
Received: 22 April 2013
Revised: 13 May 2014
Accepted: 29 July 2014
Published: 16 May 2015
Communicated by Martin Ostoja-Starzewski
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Authors |
| Daniel Morales-Silva | |
| School of Science Information Technology and Engineering Federation University Mt. Helen VIC 3353 Australia |
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| 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 |
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