The properties of generalized convexity are studied in this paper,as well as an existence Theorem of solutions for a type of generalized quasi-variational inequality is then abtained.
Taking advantage of result in [1], this paper studied generalized quasi variational inequalities on paracompact sets, unified and extended corresponding results in [4-6].
In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence t...In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].展开更多
The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the on...The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.展开更多
In this paper, some existence theorems of a solution for generalized vector quasivariational-like inequalities without any monotonity conditions in a noncompact topological space setting are proven by the maximal elem...In this paper, some existence theorems of a solution for generalized vector quasivariational-like inequalities without any monotonity conditions in a noncompact topological space setting are proven by the maximal element theorem.展开更多
We consider a class of mathematical programs governed by parameterized quasi-variational inequalities(QVI).The necessary optimality conditions for the optimization problem with QVI constraints are reformulated as a sy...We consider a class of mathematical programs governed by parameterized quasi-variational inequalities(QVI).The necessary optimality conditions for the optimization problem with QVI constraints are reformulated as a system of nonsmooth equations under the linear independence constraint qualification and the strict slackness condition.A set of second order sufficient conditions for the mathematical program with parameterized QVI constraints are proposed,which are demonstrated to be sufficient for the second order growth condition.The strongly BD-regularity for the nonsmooth system of equations at a solution point is demonstrated under the second order sufficient conditions.The smoothing Newton method in Qi-Sun-Zhou [2000] is employed to solve this nonsmooth system and the quadratic convergence is guaranteed by the strongly BD-regularity.Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this class of optimization problems.展开更多
This Paper gives a Fan’s type minimax theorem, a nearest point theorem and two existence theorems of solutions for a kind of generalized quasi-variational inequalities in H-spaces without any linear structure.
The definitions of S-KKM property and Γ-invariable property for multi-valued map- ping are established, and by which, a new almost fixed point theorem and several fixed point theorems on Haudorff locally G-convex uni...The definitions of S-KKM property and Γ-invariable property for multi-valued map- ping are established, and by which, a new almost fixed point theorem and several fixed point theorems on Haudorff locally G-convex uniform space are obtained, and a quasi-variational inequality theorem for acyclic map on Hausdorff Φ-space is proved. Our results improve and generalize the corresponding results in recent literatures.展开更多
文摘The properties of generalized convexity are studied in this paper,as well as an existence Theorem of solutions for a type of generalized quasi-variational inequality is then abtained.
文摘Taking advantage of result in [1], this paper studied generalized quasi variational inequalities on paracompact sets, unified and extended corresponding results in [4-6].
文摘In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].
文摘The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.
基金the National Natural Science Foundation of China (10171118)the Education Committee project Research Foundation of Chongqing (030801)and the Science Committee project Research Foundation of Chongqing (8409)
文摘In this paper, some existence theorems of a solution for generalized vector quasivariational-like inequalities without any monotonity conditions in a noncompact topological space setting are proven by the maximal element theorem.
基金supported by National Natural Science Foundation of China (Grant No.11071029)the Fundamental Research Funds for the Central Universities
文摘We consider a class of mathematical programs governed by parameterized quasi-variational inequalities(QVI).The necessary optimality conditions for the optimization problem with QVI constraints are reformulated as a system of nonsmooth equations under the linear independence constraint qualification and the strict slackness condition.A set of second order sufficient conditions for the mathematical program with parameterized QVI constraints are proposed,which are demonstrated to be sufficient for the second order growth condition.The strongly BD-regularity for the nonsmooth system of equations at a solution point is demonstrated under the second order sufficient conditions.The smoothing Newton method in Qi-Sun-Zhou [2000] is employed to solve this nonsmooth system and the quadratic convergence is guaranteed by the strongly BD-regularity.Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this class of optimization problems.
基金the Foundation of the Technology Commission of Zhejiang Province, China.(No.19990500), the National Natural Science Foundation
文摘This Paper gives a Fan’s type minimax theorem, a nearest point theorem and two existence theorems of solutions for a kind of generalized quasi-variational inequalities in H-spaces without any linear structure.
基金the National Natural Science Foundation of China (No.10361005)
文摘The definitions of S-KKM property and Γ-invariable property for multi-valued map- ping are established, and by which, a new almost fixed point theorem and several fixed point theorems on Haudorff locally G-convex uniform space are obtained, and a quasi-variational inequality theorem for acyclic map on Hausdorff Φ-space is proved. Our results improve and generalize the corresponding results in recent literatures.
