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Pré-Publication, Document De Travail Année : 2024

Convergence rates for the moment-SoS hierarchy


We introduce a comprehensive framework for analyzing convergence rates for infinite dimensional linear programming problems (LPs) within the context of the moment-sum-of-squares hierarchy. Our primary focus is on extending the existing convergence rate analysis, initially developed for static polynomial optimization, to the more general and challenging domain of the generalized moment problem. We establish an easy-to-follow procedure for obtaining convergence rates. Our methodology is based on, firstly, a state-of-the-art degree bound for Putinar's Positivstellensatz, secondly, quantitative polynomial approximation bounds, and, thirdly, a geometric Slater condition on the infinite dimensional LP. We address a broad problem formulation that encompasses various applications, such as optimal control, volume computation, and exit location of stochastic processes. We illustrate the procedure at these three problems and, using a recent improvement on effective versions of Putinar's Positivstellensatz, we improve existing convergence rates.
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Dates et versions

hal-04430952 , version 1 (01-02-2024)


  • HAL Id : hal-04430952 , version 1


Corbinian Schlosser, Matteo Tacchi, Alexey Lazarev. Convergence rates for the moment-SoS hierarchy. 2024. ⟨hal-04430952⟩
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