In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient proje...In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.展开更多
This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual com...This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual complementarity function associated with second-order cone.We show that the ERM model has bounded level sets under the stochastic weak R0-property.We further derive some error bound results under either the strong monotonicity or some kind of constraint qualifications.Then,we apply the Monte Carlo approximation techniques to solve the ERM model and establish a comprehensive convergence analysis.Furthermore,we report some numerical results on a stochastic second-order cone model for optimal power flow in radial networks.展开更多
In this paper, we consider a class of the stochastic linear complementarity problems （SLCPs） with finitely many elements. A feasible semismooth damped Gauss-Newton al- gorithm for the SLCP is proposed. The global an...In this paper, we consider a class of the stochastic linear complementarity problems （SLCPs） with finitely many elements. A feasible semismooth damped Gauss-Newton al- gorithm for the SLCP is proposed. The global and locally quadratic convergence of the proposed algorithm are obtained under suitable conditions. Some numerical results are reported in this paper, which confirm the good theoretical properties of the proposed al- gorithm.Mathematics subject classification： 90C33, 65K10.展开更多
文摘In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.
基金This work was supported in part by the National Natural Science Foundation of China(Nos.71831008,11671250,11431004 and 11601458)Humanity and Social Science Foundation of Ministry of Education of China(No.15YJA630034)+2 种基金Shandong Province Natural Science Fund(No.ZR2014AM012)Higher Educational Science and Technology Program of Shandong Province(No.J13LI09)Scientific Research of Young Scholar of Qufu Normal University(No.XKJ201315).
文摘This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual complementarity function associated with second-order cone.We show that the ERM model has bounded level sets under the stochastic weak R0-property.We further derive some error bound results under either the strong monotonicity or some kind of constraint qualifications.Then,we apply the Monte Carlo approximation techniques to solve the ERM model and establish a comprehensive convergence analysis.Furthermore,we report some numerical results on a stochastic second-order cone model for optimal power flow in radial networks.
基金Acknowledgments. This project is supported by National Natural Science Foundation of China （11071041） and Fujian Natural Science Foundation （2009J01002）.
文摘In this paper, we consider a class of the stochastic linear complementarity problems （SLCPs） with finitely many elements. A feasible semismooth damped Gauss-Newton al- gorithm for the SLCP is proposed. The global and locally quadratic convergence of the proposed algorithm are obtained under suitable conditions. Some numerical results are reported in this paper, which confirm the good theoretical properties of the proposed al- gorithm.Mathematics subject classification： 90C33, 65K10.
