In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, furt...In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, further the rationality is given. When the underlying function is Lipschitz continuous, we acquire a projection and contraction algorithm to solve the approximation problem. In the end, the method is applied to some numerical experiments and the effectiveness of the algorithm is verified.展开更多
Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the bounded mean oscillation(BMO)functions can be obtained from th...Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the bounded mean oscillation(BMO)functions can be obtained from their weighted variational estimates,we establish the similar variational estimates for the commutators of the BMO functions with rough singular integrals,which do not admit any weighted variational estimates.The proof involves several Littlewood-Paley-type inequalities with the commutators as well as Bony decomposition and related para-product estimates.展开更多
文摘In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, further the rationality is given. When the underlying function is Lipschitz continuous, we acquire a projection and contraction algorithm to solve the approximation problem. In the end, the method is applied to some numerical experiments and the effectiveness of the algorithm is verified.
基金This research is partly supported by the National Natural Science Foundation of China under Grant Nos. 71171027 and 11071028, the Fundamental Research Funds for the Central Universities under Grant No. DUT11SX11, and the Key Project of the National Natural Science Foundation of China under Grant No. 71031002.
基金supported by National Natural Science Foundation of China(Grant Nos.11871096,11471033,11571160 and 11601396)Thousand Youth Talents Plan of China(Grant No.429900018101150(2016))+1 种基金Funds for Talents of China(Grant No.413100002)the Fundamental Research Funds for the Central Universities and Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130003110003)。
文摘Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the bounded mean oscillation(BMO)functions can be obtained from their weighted variational estimates,we establish the similar variational estimates for the commutators of the BMO functions with rough singular integrals,which do not admit any weighted variational estimates.The proof involves several Littlewood-Paley-type inequalities with the commutators as well as Bony decomposition and related para-product estimates.
