Penalized sample average approximation methods for stochastic programs in economic and secure dispatch of a power system

2016 ◽  
Vol 13 (3) ◽  
pp. 393-422 ◽  
Author(s):  
X. J. Tong ◽  
H. Xu ◽  
F. F. Wu ◽  
Z. Zhao
Keyword(s):  
Power System ◽  
Sample Average Approximation ◽  
Approximation Methods ◽  
Stochastic Programs ◽  
Sample Average ◽  
Average Approximation

SAMPLE AVERAGE APPROXIMATION METHODS FOR A CLASS OF STOCHASTIC VARIATIONAL INEQUALITY PROBLEMS

2010 ◽  
Vol 27 (01) ◽  
pp. 103-119 ◽  
Author(s):  
HUIFU XU
Keyword(s):  
Variational Inequality ◽  
Complementarity Problems ◽  
Sample Average Approximation ◽  
Variational Inequality Problems ◽  
Stochastic Programs ◽  
Stochastic Variational Inequality ◽  
Convergence Results ◽  
Sample Average ◽  
Stochastic Constraints ◽  
Average Approximation

In this paper we apply the well known sample average approximation (SAA) method to solve a class of stochastic variational inequality problems (SVIPs). We investigate the existence and convergence of a solution to the sample average approximated SVIP. Under some moderate conditions, we show that the sample average approximated SVIP has a solution with probability one and with probability approaching one exponentially fast with the increase of sample size, the solution converges to its true counterpart. Finally, we apply the existence and convergence results to SAA method for solving a class of stochastic nonlinear complementarity problems and stochastic programs with stochastic constraints.

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