In this paper,we consider the second-order cone tensor eigenvalue complementarity problem(SOCTEiCP)and present three different reformulations to the model under consideration.Specifically,for the general SOCTEiCP,we ...In this paper,we consider the second-order cone tensor eigenvalue complementarity problem(SOCTEiCP)and present three different reformulations to the model under consideration.Specifically,for the general SOCTEiCP,we first show its equivalence to a particular variational inequality under reasonable conditions.A notable benefit is that such a reformulation possibly provides an efficient way for the study of properties of the problem.Then,for the symmetric and sub-symmetric SOCTEiCPs,we reformulate them as appropriate nonlinear programming problems,which are extremely beneficial for designing reliable solvers to find solutions of the considered problem.Finally,we report some preliminary numerical results to verify our theoretical results.展开更多
In this paper, based on the second-order sufficient condition, the Clarke's generalized Jacobian of the Karush-Kuhn-Tucker system of the second-order cone constrained variational inequality (SOCCVI) problem that i...In this paper, based on the second-order sufficient condition, the Clarke's generalized Jacobian of the Karush-Kuhn-Tucker system of the second-order cone constrained variational inequality (SOCCVI) problem that is nonsingular is proved by us. A modified Newton method with Armijo line search is presented. Three illustrative examples are given to show how the modified Newton method works.展开更多
基金the National Natural Science Foundation of China(Nos.11171083,11301123,and 11571087)the Natural Science Foundation of Zhejiang Province(Nos.LZ14A010003 and LY17A010028).
文摘In this paper,we consider the second-order cone tensor eigenvalue complementarity problem(SOCTEiCP)and present three different reformulations to the model under consideration.Specifically,for the general SOCTEiCP,we first show its equivalence to a particular variational inequality under reasonable conditions.A notable benefit is that such a reformulation possibly provides an efficient way for the study of properties of the problem.Then,for the symmetric and sub-symmetric SOCTEiCPs,we reformulate them as appropriate nonlinear programming problems,which are extremely beneficial for designing reliable solvers to find solutions of the considered problem.Finally,we report some preliminary numerical results to verify our theoretical results.
文摘In this paper, based on the second-order sufficient condition, the Clarke's generalized Jacobian of the Karush-Kuhn-Tucker system of the second-order cone constrained variational inequality (SOCCVI) problem that is nonsingular is proved by us. A modified Newton method with Armijo line search is presented. Three illustrative examples are given to show how the modified Newton method works.
