A sample average approximation regularization method for a stochastic mathematical program with general vertical complementarity constraints
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Jie Zhang [1] ; Ya-qi Zhang [1] ; Li-wei Zhang [2]
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[1] Liaoning Normal University
Liaoning Normal University
China
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[2] Dalian University of Technology
Dalian University of Technology
China
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- Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 280, Nº 1 (15 May 2015), 2015, págs. 202-216
- Idioma: inglés
- DOI: 10.1016/j.cam.2014.11.057
- Texto completo no disponible (Saber más ...)
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Resumen
Based on the log-exponential function, a sample average approximation (SAA) regularization method is proposed for solving a stochastic mathematical program with general vertical complementarity constraints (SMPVCC) considered by Birbil et al. (2006). Detailed convergence analysis of this method is investigated. It is demonstrated that under some regularity conditions, any accumulation point of the sequence of optimal solutions of SAA regularized problem is almost surely an optimal solution of the SMPVCC as the parameter tends to zero and the sample size tends to infinity. Furthermore, the optimal value sequence of SAA regularized problem converges to the optimal value of SMPVCC with exponential convergence rate with probability one and a sequence of stationary points of regularized SAA problem converges almost surely to a stationary point of SMPVCC. Finally, we show that a stochastic Stackelberg game can be formulated as a SMPVCC problem and an equilibrium solution can be obtained by the method proposed
