scholarly journals Expected Residual Minimization Method for Stochastic Generalized Complementary Problems

2012 ◽  
Vol 01 (01) ◽  
pp. 12-17
Author(s):  
美菊 罗
Keyword(s):  
Minimization Method ◽  
Expected Residual Minimization ◽  
Complementary Problems ◽  
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 Estimation of Reverberation Time in Classrooms Using the Residual Minimization Method

2017 ◽  
Vol 42 (4) ◽  
pp. 609-617 ◽  
Author(s):  
Artur Nowoświat ◽  
Marcelina Olechowska
Keyword(s):  
Computer Simulations ◽  
Acoustic Field ◽  
Analytical Methods ◽  
Room Acoustics ◽  
Reverberation Time ◽  
Minimization Method ◽  
Theoretical Methods ◽  
Residual Minimization

Abstract The objective of the residual minimization method is to determine a coefficient correcting the Sabine’s model. The Sabine’s equation is the most commonly applied formula in the designing process of room acoustics with the use of analytical methods. The correction of this model is indispensable for its application in rooms having non-diffusive acoustic field. The authors of the present paper will be using the residual minimization method to work out a suitable correction to be applied for classrooms. For this purpose, five different poorly dampened classrooms were selected, in which the measurements of reverberation time were carried out, and for which reverberation time was calculated with the use of theoretical methods. Three of the selected classrooms had the cubic volume of 258.5 m3 and the remaining two had the cubic volume of 190.8 m3. It was sufficient to estimate the correction for the Sabine’s equation. To verify the results, three other classrooms were selected, in which also the measurements of reverberation time were carried out. The results were verified by means of real measurements of reverberation time and by means of computer simulations in the program ODEON.

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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