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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00314868" target="_blank" >RIV/68407700:21230/17:00314868 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.sysconle.2016.11.010" target="_blank" >http://dx.doi.org/10.1016/j.sysconle.2016.11.010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.sysconle.2016.11.010" target="_blank" >10.1016/j.sysconle.2016.11.010</a>

Result language
angličtina
Original language name
Convergence rates of moment-sum-of-squares hierarchies for optimal control problems
Original language description
We study the convergence rate of the moment-sum-of-squares hierarchy of semidefinite programs for optimal control problems with polynomial data. It is known that this hierarchy generates 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∕loglogd). 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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