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 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.
© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2020. Received 21 July 2019; Accepted 11 August 2020; Published 14 October 2020. The authors thank Fangzhou Xiao and two anonymous referees for helpful feedback. R.M. was supported in part by an NSF Graduate Research Fellowship, NSF grants CCF-1350590 and CCF-1637598, and AFOSR grant FA9550-16-1-0210. V.C. was supported in part by NSF grants CCF-1350590 and CCF-1637598, AFOSR grant FA9550-16-1-0210, and a Sloan Research Fellowship. A.W. was supported in part by NSF grant CCF-1637598.
Murray, R., Chandrasekaran, V. & Wierman, A. Publisher Correction to: Signomial and polynomial optimization via relative entropy and partial dualization. Math. Prog. Comp. 13, 297–299 (2021). https://doi.org/10.1007/s12532-021-00201-1