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A smoothing penalized sample average approximation method for stochastic programs with second order stochastic dominance constraints

A smoothing penalized sample average approximation method for stochastic programs with second order stochastic dominance constraints
A smoothing penalized sample average approximation method for stochastic programs with second order stochastic dominance constraints
In this paper, we propose a smoothing penalized sample average approximation (SAA) method for solving a stochastic minimization problem with second-order dominance constraints. The basic idea is to use sample average to approximate the expected values of the underlying random functions and then reformulate the discretized problem as an ordinary nonlinear programming problem with finite number of constraints. An exact penalty function method is proposed to deal with the latter and an elementary smoothing technique is used to tackle the nonsmoothness of the plus function and the exact penalty function. We investigate the convergence of the optimal value obtained from solving the smoothed penalized sample average approximation problem as sample size increases and show that with probability approaching to one at exponential rate with the increase of sample size the optimal value converges to its true counterpart. Some preliminary numerical results are reported.


Read More: http://www.worldscientific.com/doi/abs/10.1142/S0217595913400022
0217-5959
1-25
Sun, Hailin
eee2e5fb-018b-45d4-b599-08209509663c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Wang, Yong
a7913cc9-1250-4f71-ab1f-93480043bb6a
Sun, Hailin
eee2e5fb-018b-45d4-b599-08209509663c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Wang, Yong
a7913cc9-1250-4f71-ab1f-93480043bb6a

Sun, Hailin, Xu, Huifu and Wang, Yong (2013) A smoothing penalized sample average approximation method for stochastic programs with second order stochastic dominance constraints. Asia-Pacific Journal of Operational Research, 30 (3), 1-25. (doi:10.1142/S0217595913400022).

Record type: Article

Abstract

In this paper, we propose a smoothing penalized sample average approximation (SAA) method for solving a stochastic minimization problem with second-order dominance constraints. The basic idea is to use sample average to approximate the expected values of the underlying random functions and then reformulate the discretized problem as an ordinary nonlinear programming problem with finite number of constraints. An exact penalty function method is proposed to deal with the latter and an elementary smoothing technique is used to tackle the nonsmoothness of the plus function and the exact penalty function. We investigate the convergence of the optimal value obtained from solving the smoothed penalized sample average approximation problem as sample size increases and show that with probability approaching to one at exponential rate with the increase of sample size the optimal value converges to its true counterpart. Some preliminary numerical results are reported.


Read More: http://www.worldscientific.com/doi/abs/10.1142/S0217595913400022

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More information

Published date: June 2013
Organisations: Operational Research

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Local EPrints ID: 390728
URI: http://eprints.soton.ac.uk/id/eprint/390728
ISSN: 0217-5959
PURE UUID: 58a86013-5e6e-49ab-9fef-b5bb04e04f7d
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

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Date deposited: 06 Apr 2016 14:37
Last modified: 09 Jan 2022 03:12

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Contributors

Author: Hailin Sun
Author: Huifu Xu ORCID iD
Author: Yong Wang

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