Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: TTRISK: Tensor Train Decomposition Algorithm for Risk Averse
  Optimization   This article develops a new algorithm named TTRISK to solve high-dimensional
risk-averse optimization problems governed by differential equations (ODEs
and/or PDEs) under uncertainty. As an example, we focus on the so-called
Conditional Value at Risk (CVaR), but the approach is equally applicable to
other coherent risk measures. Both the full and reduced space formulations are
considered. The algorithm is based on low rank tensor approximations of random
fields discretized using stochastic collocation. To avoid non-smoothness of the
objective function underpinning the CVaR, we propose an adaptive strategy to
select the width parameter of the smoothed CVaR to balance the smoothing and
tensor approximation errors. Moreover, unbiased Monte Carlo CVaR estimate can
be computed by using the smoothed CVaR as a control variate. To accelerate the
computations, we introduce an efficient preconditioner for the KKT system in
the full space formulation.The numerical experiments demonstrate that the
proposed method enables accurate CVaR optimization constrained by large-scale
discretized systems. In particular, the first example consists of an elliptic
PDE with random coefficients as constraints. The second example is motivated by
a realistic application to devise a lockdown plan for United Kingdom under
COVID-19. The results indicate that the risk-averse framework is feasible with
the tensor approximations under tens of random variables.

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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg