Expected Residual Minimization (ERM)

2021 ◽  
pp. 213-232
Author(s):  
Joachim Gwinner ◽  
Baasansuren Jadamba ◽  
Akhtar A. Khan ◽  
Fabio Raciti
Keyword(s):  
Expected Residual Minimization ◽  
Residual Minimization

scholarly journals Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Hui-Qiang Ma ◽  
Nan-Jing Huang
Keyword(s):  
Sample Average Approximation ◽  
Gap Function ◽  
Stationary Points ◽  
Quasivariational Inequality ◽  
Minimization Method ◽  
Limiting Behavior ◽  
Regularized Gap Function ◽  
Expected Residual Minimization ◽  
Sample Average ◽  
Residual Minimization

We consider the expected residual minimization method for a class of stochastic quasivariational inequality problems (SQVIP). The regularized gap function for quasivariational inequality problem (QVIP) is in general not differentiable. We first show that the regularized gap function is differentiable and convex for a class of QVIPs under some suitable conditions. Then, we reformulate SQVIP as a deterministic minimization problem that minimizes the expected residual of the regularized gap function and solve it by sample average approximation (SAA) method. Finally, we investigate the limiting behavior of the optimal solutions and stationary points.

scholarly journals Properties of Expected Residual Minimization Model for a Class of Stochastic Complementarity Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mei-Ju Luo ◽  
Yuan Lu
Keyword(s):  
Complementarity Problems ◽  
Random Parameter ◽  
Quasi Monte Carlo ◽  
Expected Residual Minimization ◽  
Derivative Free ◽  
Residual Functions ◽  
Minimum Sensitivity ◽  
Residual Minimization ◽  
Boundedness Of Solution ◽  
Stochastic Complementarity Problems

Expected residual minimization (ERM) model which minimizes an expected residual function defined by an NCP function has been studied in the literature for solving stochastic complementarity problems. In this paper, we first give the definitions of stochasticP-function, stochasticP0-function, and stochastic uniformlyP-function. Furthermore, the conditions such that the function is a stochasticPP0-function are considered. We then study the boundedness of solution set and global error bounds of the expected residual functions defined by the “Fischer-Burmeister” (FB) function and “min” function. The conclusion indicates that solutions of the ERM model are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in stochastic complementarity problems. On the other hand, we employ quasi-Monte Carlo methods and derivative-free methods to solve ERM model.

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