Paper Info
Title
RELATIVE ENTROPY RELAXATIONS FOR SIGNOMIAL OPTIMIZATION
Abstract
Signomial programs (SPs) are optimization problems specified in terms of signomials, which are weighted sums of exponentials composed with linear functionals of a decision variable. SPs are nonconvex optimization problems in general, and families of NP-hard problems can be reduced to SPs. In this paper we describe a hierarchy of convex relaxations to obtain successively tighter lower bounds of the optimal value of SPs. This sequence of lower bounds is computed by solving increasingly larger-sized relative entropy optimization problems, which are convex programs specified in terms of linear and relative entropy functions. Our approach relies crucially on the observation that the relative entropy function, by virtue of its joint convexity with respect to both arguments, provides a convex parametrization of certain sets of globally nonnegative signomials with efficiently computable nonnegativity certificates via the arithmetic-geometric-mean inequality. By appealing to representation theorems from real algebraic geometry, we show that our sequences of lower bounds converge to the global optima for broad classes of SPs. Finally, we also demonstrate the effectiveness of our methods via numerical experiments.
Year
DOI
Venue
2016
10.1137/140988978
SIAM JOURNAL ON OPTIMIZATION
Keywords
DocType
Volume
arithmetic-geometric-mean inequality,convex optimization,geometric programming,global optimization,real algebraic geometry
Journal
26
Issue
ISSN
Citations 
2
1052-6234
6
PageRank 
References 
Authors
0.46
9
2
Name
Order
Citations
PageRank
Venkat Chandrasekaran171637.92
Parikshit Shah231518.43