Slow convergence of the moment-SOS hierarchy for an elementary polynomial optimization problem

2024/03/13 by Henrion, Didier, Franc, Adrien Le, Magron, Victor · 3 citations
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2403.08329

Abstract

We describe a parametric univariate quadratic optimization problem for which the moment-SOS hierarchy has finite but increasingly slow convergence when the parameter tends to its limit value. We estimate the order of finite convergence as a function of the parameter.

Cited by

• Solving Stengle's Example in Rational Arithmetic: Exact Values of the Moment-SOS Relaxations
• Finite Convergence of the Moment-SOS Hierarchy on the Product of Spheres
• Lagrange multiplier expressions for matrix polynomial optimization and tight relaxations

Related

• Finite convergence of the Moment-SOS hierarchy for polynomial matrix optimization
• Convergence rates for the moment-SoS hierarchy
• Convergence rate for linear minimizer-estimators in the moment-sum-of-squares hierarchy
• On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences
• A note on the computational complexity of the moment-SOS hierarchy for polynomial optimization