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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.
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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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