Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When th...

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Veröffentlicht in:Mathematical programming Jg. 163; H. 1-2; S. 169 - 212
1. Verfasser: Guigues, Vincent
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2017
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Confidence intervals
Convex analysis
Descent
Euclidean space
Expected utility
Full Length Paper
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Polyhedra
Risk
Simulation
Stochastic models
Stochasticity
Studies
Theoretical
90C90
90C15
Stochastic optimization
Robust Stochastic Approximation
Multistep Stochastic Mirror Descent
Risk measures
ISSN:0025-5610, 1436-4646
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic Mirror Descent algorithm and obtain confidence intervals on both the optimal values and optimal solutions. Numerical simulations show that our confidence intervals are much less conservative and are quicker to compute than previously obtained confidence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-016-1060-0