Dr Mareike Dressler

Title: Algebraic Perspectives on Signomial Optimization

Abstract:
Signomials generalize polynomials by allowing arbitrary real exponents, at the expense of restricting the resulting function to the positive orthant. In this talk, I present a signomial Positivstellensatz based on conditional “sums of arithmetic-geometric exponentials” (SAGE). The Positivstellensatz applies to compact sets which need not be convex or even basic semi-algebraic. In the first part of the talk, I explain how this result is derived through the newly-defined concept of signomial rings. Then I show how the same concept leads to a novel convex relaxation hierarchy of lower bounds for signomial optimization. These relaxations (which are based on relative entropy programming) can be solved more reliably than those arising from earlier SAGE-based Positivstellensätze. Moreover, this increase in reliability comes at no apparent cost of longer solver runtimes or worse bounds. Numerical examples are provided to illustrate the performance of the hierarchy on a problem in chemical reaction networks. To conclude, I provide an outlook on how any (hierarchical) inner-approximation of the signomial nonnegativity cone yields upper bounds for signomial optimization.

Bio:

Mareike Dressler is a Lecturer in the School of Mathematics and Statistics at the University of New South Wales, Sydney. She received her PhD from the Goethe University Frankfurt. Prior to joining UNSW, she was a postdoctoral fellow at Brown University (ICERM), a visiting assistant professor at University of California, San Diego, and a postdoctoral researcher at the Max Planck Institute for Mathematics in the Sciences, Leipzig. Mareike’s research is in mathematical optimization and real and computational algebraic geometry. She is particularly interested in developing algebraic and geometrical tools to design improved computational optimization methods and algorithms

WED 23 NOVEMBER 16:00 – 17:00 PM AEDT MELBOURNE ONLINE

ZOOM MEETING ID: 873 1557 5255; PASSWORD: 778635