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An adaptive trust-region approach for nonlinear stochastic optimisation with an application in discrete choice theory

Authors: Fabian Bastin

Published in: Dagstuhl Seminar Proceedings, Volume 5031, Algorithms for Optimization with Incomplete Information (2005)

Abstract

We consider stochastic nonlinear programs, restricting ourself to differentiable, but possibly non-convex, problems. The non-convexity leads us to consider non-linear approaches, designed to find second-order critical solutions. We focus here on the use of trust-region approaches when solving a sample average approximation, and adapt the technique to only use sub-samples when possible, adjusting the sample size at each iteration. We show that under reasonable assumptions, we solve the original SAA problem. We also consider an extension to the estimation of mixed logit models, that are popular in discrete choice theory when the population heterogeneity is taken into account. We present numerical experimentations underlining the practical interest of the method. We finally examine some avenues and preliminary experimentations for future research.

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Fabian Bastin. An adaptive trust-region approach for nonlinear stochastic optimisation with an application in discrete choice theory. In Algorithms for Optimization with Incomplete Information. Dagstuhl Seminar Proceedings, Volume 5031, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{bastin:DagSemProc.05031.3,
  author =	{Bastin, Fabian},
  title =	{{An adaptive trust-region approach for nonlinear stochastic optimisation with an application in discrete choice theory}},
  booktitle =	{Algorithms for Optimization with Incomplete Information},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5031},
  editor =	{Susanne Albers and Rolf H. M\"{o}hring and Georg Ch. Pflug and R\"{u}diger Schultz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05031.3},
  URN =		{urn:nbn:de:0030-drops-559},
  doi =		{10.4230/DagSemProc.05031.3},
  annote =	{Keywords: Nonlinear Stochastic Programming , Monte-Carlo , Mixed Logit , Discrete Choice , Trust-Region}
}

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An adaptive trust-region approach for nonlinear stochastic optimisation with an application in discrete choice theory

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