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An approximate approach of global optimization for polynomial programming problems

โœ Scribed by Han-Lin Li; Ching-Ter Chang

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
626 KB
Volume
107
Category
Article
ISSN
0377-2217

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โœฆ Synopsis

Many methods for solving polynomial programming problems can only find locally optimal solutions. This paper proposes a method for finding the approximately globally optimal solutions of polynomial programs. Representing a bounded continuous variable xi as the addition of a discrete variable dj and a small variable E,, a polynomial term xixi can be expanded as the sum of d,xj, dj&; and E,E,. A procedure is then developed to fully linearize din, and djci, and to approximately linearize E;C~ with an error below a pre-specified tolerance. This linearization procedure can also be extended to higher order polynomial programs. Several polynomial programming examples in the literature are tested to demonstrate that the proposed method can systematically solve these examples to find the global optimum within a pre-specified error.

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