In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of ...In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of the functions at a given feasible point. The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case. As in classical case so called constraint qualifications have to be imposed on the constraint functions to guarantee that for a given local minimizer of the original problem the nullvector is an optimal solution of the corresponding 'quasilinearized' problem. In this paper, constraint qualifications for inequality constrained quasi differentiable programming problems of type min {f(x)|g(x)≤0} are considered, where f and g are qusidifferentiable functions in the sense of Demyanov. Various constraint qualifications for this problem are presented and a new one is proposed. The relations among these conditions are investigated. Moreover, a Wolf dual problem for this problem is introduced, and the corresponding dual theorems are given.展开更多
Firstly,the notion of the left-left Yetter-Drinfeld quasicomodule M=(M,·,ρ)over a Hopf coquasigroup H is given,which generalizes the left-left Yetter-Drinfeld module over Hopf algebras.Secondly,the braided monoi...Firstly,the notion of the left-left Yetter-Drinfeld quasicomodule M=(M,·,ρ)over a Hopf coquasigroup H is given,which generalizes the left-left Yetter-Drinfeld module over Hopf algebras.Secondly,the braided monoidal category HHYDQCM is introduced and the specific structure maps are given.Thirdly,Sweedler's dual of infinite-dimensional Hopf algebras in HHYDQCM is discussed.It proves that if(B,mB,μB,ΔB,εB)is a Hopf algebra in HHYDQCM with antipode SB,then(B^0,(mB0)^op,εB^*,(ΔB0)^op,μB^*)is a Hopf algebra in HHYDQCM with antipode SB^*,which generalizes the corresponding results over Hopf algebras.展开更多
文摘In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of the functions at a given feasible point. The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case. As in classical case so called constraint qualifications have to be imposed on the constraint functions to guarantee that for a given local minimizer of the original problem the nullvector is an optimal solution of the corresponding 'quasilinearized' problem. In this paper, constraint qualifications for inequality constrained quasi differentiable programming problems of type min {f(x)|g(x)≤0} are considered, where f and g are qusidifferentiable functions in the sense of Demyanov. Various constraint qualifications for this problem are presented and a new one is proposed. The relations among these conditions are investigated. Moreover, a Wolf dual problem for this problem is introduced, and the corresponding dual theorems are given.
基金The National Natural Science Foundation of China(No.11371088,11571173,11871144)。
文摘Firstly,the notion of the left-left Yetter-Drinfeld quasicomodule M=(M,·,ρ)over a Hopf coquasigroup H is given,which generalizes the left-left Yetter-Drinfeld module over Hopf algebras.Secondly,the braided monoidal category HHYDQCM is introduced and the specific structure maps are given.Thirdly,Sweedler's dual of infinite-dimensional Hopf algebras in HHYDQCM is discussed.It proves that if(B,mB,μB,ΔB,εB)is a Hopf algebra in HHYDQCM with antipode SB,then(B^0,(mB0)^op,εB^*,(ΔB0)^op,μB^*)is a Hopf algebra in HHYDQCM with antipode SB^*,which generalizes the corresponding results over Hopf algebras.
