Alternating direction method of multipliers for real and complex polynomial optimization models
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AbstractIn this paper, we propose a new method for polynomial optimization with real or complex decision variables. The main ingredient of the approach is to apply the classical alternating direction method of multipliers based on the augmented Lagrangian function. In this particular case, this allows us to fully exploit the multi-block structure of the polynomial functions, even though the optimization model encountered is highly non-linear and non-convex. The new method is shown to be convergent under some conditions, and the numerical results show that the algorithm returns high quality solutions and runs much faster than the two other competing algorithms.
All Author(s) ListJiang B, Ma SQ, Zhang SZ
Journal nameOptimization
Year2014
Month6
Day3
Volume Number63
Issue Number6
PublisherTAYLOR & FRANCIS LTD
Pages883 - 898
ISSN0233-1934
eISSN1029-4945
LanguagesEnglish-United Kingdom
Keywords15A69; 65F30; 90C26; 90C30; alternating direction method of multipliers; optimization with complex variables; polynomial optimization
Web of Science Subject CategoriesMathematics; Mathematics, Applied; MATHEMATICS, APPLIED; Operations Research & Management Science; OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Last updated on 2021-19-01 at 00:00