A bounded degree hierarchy with SOS relaxations for classes of polynomial optimization problems

Date: 15:30-16:30, 02 October 2025

Venue: Room 301, A5, Institute of Mathematics

Abstract: In this talk, we consider separable plus lower degree (SPLD) polynomials, by which we mean polynomials that have the decomposition of the sum of univariate polynomials (in different variables) and a polynomial whose degree is lower than the one of the separable polynomial. A type of bounded degree SOS hierarchy, referred to as BSOS-SPLD, is proposed to efficiently solve optimization problems involving SPLD polynomials. Numerical experiments on several benchmark problems indicate that the proposed method yields better performance than the standard bounded degree SOS hierarchy (Lasserre et al. in EURO J Comput Optim 5:87–117, 2017). An exact SOS relaxation for a class of convex SPLD polynomial optimization problems is also proposed. Finally, we present an application of SPLD polynomials to convex polynomial regression problems arising in statistics.