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Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

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arxiv 1609.02762 v1 pith:ZLLPVVBK submitted 2016-09-09 math.OC

classification math.OC
keywords controlconvergencehierarchiesoptimalproblemproblemsratecontinuous-time
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We study the convergence rate of moment-sum-of-squares hierarchies of semidefinite programs for optimal control problems with polynomial data. It is known that these hierarchies generate polynomial under-approximations to the value function of the optimal control problem and that these under-approximations converge in the L1 norm to the value function as their degree d tends to infinity. We show that the rate of this convergence is O(1/ log log d). We treat in detail the continuous-time infinite-horizon discounted problem and describe in brief how the same rate can be obtained for the finite-horizon continuous-time problem and for the discrete-time counterparts of both problems.

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  1. Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra

    quant-ph 2026-06 unverdicted novelty 8.0 of 10

    Explicit convergence rates for noncommutative SOS hierarchies on the Pauli algebra are bounded using smallest roots of Krawtchouk polynomials.

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