Signomial and polynomial optimization via relative entropy and partial dualization

We describe a generalization of the Sums-of-AM/GM-Exponential (SAGE) methodology for relative entropy relaxations of constrained signomial and polynomial optimization problems. Our approach leverages the fact that SAGE certificates conveniently and transparently blend with convex duality, in a way w...

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Bibliographic Details
Published inMathematical programming computation Vol. 13; no. 2; pp. 257 - 295
Main Authors Murray, Riley, Chandrasekaran, Venkat, Wierman, Adam
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
Springer Nature B.V
Subjects
Constraints
Entropy
Full Length Paper
Global optimization
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Optimization
Polynomials
Theory of Computation
Signomial programming
Exponential cone programs
Global optimization
SAGE certificates
SOS certificates
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Summary:We describe a generalization of the Sums-of-AM/GM-Exponential (SAGE) methodology for relative entropy relaxations of constrained signomial and polynomial optimization problems. Our approach leverages the fact that SAGE certificates conveniently and transparently blend with convex duality, in a way which enables partial dualization of certain structured constraints. This more general approach retains key properties of ordinary SAGE relaxations (e.g. sparsity preservation), and inspires a projective method of solution recovery which respects partial dualization. We illustrate the utility of our methodology with a range of examples from the global optimization literature, along with a publicly available software package.
ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-020-00193-4