Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme

We study the distributionally robust stochastic optimization problem within a general framework of risk measures, in which the ambiguity set is described by a spectrum of practically used probability distribution constraints such as bounds on mean-deviation and entropic value-at-risk. We show that a...

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Main Authors: Yu, H., Sun, Jie
Format: Journal Article
Language:English
Published: AMER INST MATHEMATICAL SCIENCES-AIMS 2021
Subjects:
Online Access:http://purl.org/au-research/grants/arc/DP160102819
http://hdl.handle.net/20.500.11937/90790
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author Yu, H.
Sun, Jie
author_facet Yu, H.
Sun, Jie
author_sort Yu, H.
building Curtin Institutional Repository
collection Online Access
description We study the distributionally robust stochastic optimization problem within a general framework of risk measures, in which the ambiguity set is described by a spectrum of practically used probability distribution constraints such as bounds on mean-deviation and entropic value-at-risk. We show that a subgradient of the objective function can be obtained by solving a Finite-dimensional optimization problem, which facilitates subgradient-type algorithms for solving the robust stochastic optimization problem. We develop an algorithm for two-stage robust stochastic programming with conditional value at risk measure. A numerical example is presented to show the effectiveness of the proposed method.
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institution Curtin University Malaysia
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language English
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publishDate 2021
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spelling curtin-20.500.11937-907902023-05-11T01:50:17Z Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme Yu, H. Sun, Jie Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Operations Research & Management Science Mathematics, Interdisciplinary Applications Engineering Mathematics Stochastic optimization distributionally robust convex risk measure subgradient method two-stage optimization problem LINEAR OPTIMIZATION PROGRAMS MODELS We study the distributionally robust stochastic optimization problem within a general framework of risk measures, in which the ambiguity set is described by a spectrum of practically used probability distribution constraints such as bounds on mean-deviation and entropic value-at-risk. We show that a subgradient of the objective function can be obtained by solving a Finite-dimensional optimization problem, which facilitates subgradient-type algorithms for solving the robust stochastic optimization problem. We develop an algorithm for two-stage robust stochastic programming with conditional value at risk measure. A numerical example is presented to show the effectiveness of the proposed method. 2021 Journal Article http://hdl.handle.net/20.500.11937/90790 10.3934/jimo.2019100 English http://purl.org/au-research/grants/arc/DP160102819 AMER INST MATHEMATICAL SCIENCES-AIMS restricted
spellingShingle Science & Technology
Technology
Physical Sciences
Engineering, Multidisciplinary
Operations Research & Management Science
Mathematics, Interdisciplinary Applications
Engineering
Mathematics
Stochastic optimization
distributionally robust
convex risk measure
subgradient method
two-stage optimization problem
LINEAR OPTIMIZATION
PROGRAMS
MODELS
Yu, H.
Sun, Jie
Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme
title Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme
title_full Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme
title_fullStr Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme
title_full_unstemmed Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme
title_short Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme
title_sort robust stochastic optimization with convex risk measures: a discretized subgradient scheme
topic Science & Technology
Technology
Physical Sciences
Engineering, Multidisciplinary
Operations Research & Management Science
Mathematics, Interdisciplinary Applications
Engineering
Mathematics
Stochastic optimization
distributionally robust
convex risk measure
subgradient method
two-stage optimization problem
LINEAR OPTIMIZATION
PROGRAMS
MODELS
url http://purl.org/au-research/grants/arc/DP160102819
http://hdl.handle.net/20.500.11937/90790