Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A stochastic algorithm for deterministic multistage optimization
  problems   Several attempts to dampen the curse of dimensionnality problem of the
Dynamic Programming approach for solving multistage optimization problems have
been investigated. One popular way to address this issue is the Stochastic Dual
Dynamic Programming method (SDDP) introduced by Perreira and Pinto in 1991 for
Markov Decision Processes. Assuming that the value function is convex (for a
minimization problem), one builds a non-decreasing sequence of lower (or outer)
convex approximations of the value function. Those convex approximations are
constructed as a supremum of affine cuts. On continuous time deterministic
optimal control problems, assuming that the value function is semiconvex, Zheng
Qu, inspired by the work of McEneaney, introduced in 2013 a stochastic max-plus
scheme that builds upper (or inner) non-increasing approximations of the value
function. In this note, we build a common framework for both the SDDP and a
discrete time version of Zheng Qu's algorithm to solve deterministic multistage
optimization problems. Our algorithm generates monotone approximations of the
value functions as a pointwise supremum, or infimum, of basic (affine or
quadratic for example) functions which are randomly selected. We give
sufficient conditions on the way basic functions are selected in order to
ensure almost sure convergence of the approximations to the value function on a
set of interest.

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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org