scholarly journals A class of smoothing SAA methods for a stochastic linear complementarity problem

2012 ◽  
Vol 2 (1) ◽  
pp. 145-156
Author(s):  
Jie Zhang ◽  
◽  
Yue Wu ◽  
Liwei Zhang ◽  
◽  
...  
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Stochastic Linear Complementarity Problem

scholarly journals The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Liyan Xu ◽  
Bo Yu ◽  
Wei Liu
Keyword(s):  
Robust Optimization ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Uncertain Parameters ◽  
Distributionally Robust Optimization ◽  
Worst Case ◽  
Nonnegativity Constraints ◽  
Distributionally Robust ◽  
Stochastic Linear Complementarity Problem

We investigate the stochastic linear complementarity problem affinely affected by the uncertain parameters. Assuming that we have only limited information about the uncertain parameters, such as the first two moments or the first two moments as well as the support of the distribution, we formulate the stochastic linear complementarity problem as a distributionally robust optimization reformation which minimizes the worst case of an expected complementarity measure with nonnegativity constraints and a distributionally robust joint chance constraint representing that the probability of the linear mapping being nonnegative is not less than a given probability level. Applying the cone dual theory and S-procedure, we show that the distributionally robust counterpart of the uncertain complementarity problem can be conservatively approximated by the optimization with bilinear matrix inequalities. Preliminary numerical results show that a solution of our method is desirable.

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