The Moment-SOS hierarchy
Jean Lasserre (LAAS-MAC)
TL;DR
The paper discusses the Moment-SOS hierarchy, a mathematical framework based on the theory of moments and positive polynomials, which can solve a wide range of optimization problems with positivity and measure constraints.
Contribution
It explains the application of the Moment-SOS hierarchy to generalized moment problems and highlights its versatility across various domains.
Findings
Applicable to problems with positivity constraints on functions
Effective in solving generalized moment problems
Versatile across multiple application domains
Abstract
The Moment-SOS hierarchy initially introduced in optimization in 2000, is based on the theory of the K-moment problem and its dual counterpart, polynomials that are positive on K. It turns out that this methodology can be also applied to solve problems with positivity constraints " f (x) 0 for all x K " and/or linear constraints on Borel measures. Such problems can be viewed as specific instances of the " Generalized Problem of Moments " (GPM) whose list of important applications in various domains is endless. We describe this methodology and outline some of its applications in various domains.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Constraint Satisfaction and Optimization · Optimization and Variational Analysis