A smoothing SAA method for a stochastic mathematical program with complementarity constraints
A smoothing SAA method for a stochastic mathematical program with complementarity constraints
A smoothing sample average approximation (SAA) method based on the log-exponential function is proposed for solving a stochastic mathematical program with complementarity constraints (SMPCC) considered by Birbil et al. (S. I. Birbil, G. Gürkan, O. Listes: Solving stochastic mathematical programs with complementarity constraints using simulation, Math. Oper. Res. 31 (2006), 739–760). It is demonstrated that, under suitable conditions, the optimal solution of the smoothed SAA problem converges almost surely to that of the true problem as the sample size tends to infinity. Moreover, under a strong second-order sufficient condition for SMPCC, the almost sure convergence of Karash-Kuhn-Tucker points of the smoothed SAA problem is established by Robinson’s stability theory. Some preliminary numerical results are reported to show the efficiency of our method.
477-502
Zhang, Jie
307343f1-40bb-48f4-b9fa-a783576450da
Zhang, Li-Wei
1a6d1add-39ba-4969-8134-8f126844b5f6
Wu, Yue
e279101b-b392-45c4-b894-187e2ded6a5c
18 October 2012
Zhang, Jie
307343f1-40bb-48f4-b9fa-a783576450da
Zhang, Li-Wei
1a6d1add-39ba-4969-8134-8f126844b5f6
Wu, Yue
e279101b-b392-45c4-b894-187e2ded6a5c
Zhang, Jie, Zhang, Li-Wei and Wu, Yue
(2012)
A smoothing SAA method for a stochastic mathematical program with complementarity constraints.
Applications of Mathematics, 57 (5), .
(doi:10.1007/s10492-012-0028-5).
Abstract
A smoothing sample average approximation (SAA) method based on the log-exponential function is proposed for solving a stochastic mathematical program with complementarity constraints (SMPCC) considered by Birbil et al. (S. I. Birbil, G. Gürkan, O. Listes: Solving stochastic mathematical programs with complementarity constraints using simulation, Math. Oper. Res. 31 (2006), 739–760). It is demonstrated that, under suitable conditions, the optimal solution of the smoothed SAA problem converges almost surely to that of the true problem as the sample size tends to infinity. Moreover, under a strong second-order sufficient condition for SMPCC, the almost sure convergence of Karash-Kuhn-Tucker points of the smoothed SAA problem is established by Robinson’s stability theory. Some preliminary numerical results are reported to show the efficiency of our method.
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Accepted/In Press date: 2012
Published date: 18 October 2012
Organisations:
Centre of Excellence for International Banking, Finance & Accounting
Identifiers
Local EPrints ID: 186583
URI: http://eprints.soton.ac.uk/id/eprint/186583
ISSN: 0862-7940
PURE UUID: 364a200e-f527-4972-b57a-bb6b621cac56
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Date deposited: 13 May 2011 13:34
Last modified: 12 Nov 2024 02:41
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Author:
Jie Zhang
Author:
Li-Wei Zhang
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