Multi-Degrees in Polynomial Optimization

2022/09/21 by Rose, Kemal
#Algebraic Geometry (math.AG) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2209.10670

Abstract

We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in several variables. For fixed multi-degrees we determine the generic number of complex critical points. This serves as a measure for the algebraic complexity of the optimization problem. We also discuss computation and certification methods coming from numerical nonlinear algebra.

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