Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tropical Dynamic Programming for Lipschitz Multistage Stochastic
  Programming   We present an algorithm called Tropical Dynamic Programming (TDP) which
builds upper and lower approximations of the Bellman value functions in
risk-neutral Multistage Stochastic Programming (MSP), with independent noises
of finite supports.
  To tackle the curse of dimensionality, popular parametric variants of
Approximate Dynamic Programming approximate the Bellman value function as
linear combinations of basis functions. Here, Tropical Dynamic Programming
builds upper (resp. lower) approximations of a given value function as min-plus
linear (resp. max-plus linear) combinations of "basic functions". At each
iteration, TDP adds a new basic function to the current combination following a
deterministic criterion introduced by Baucke, Downward and Zackeri in 2018 for
a variant of Stochastic Dual Dynamic Programming.
  We prove, for every Lipschitz MSP, the asymptotic convergence of the
generated approximating functions of TDP to the Bellman value functions on sets
of interest. We illustrate this result on MSP with linear dynamics and
polyhedral costs.

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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph