Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work t...Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.展开更多
This paper aims to develop a power penalty method for a linear parabolic variational inequality （VI） in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional ...This paper aims to develop a power penalty method for a linear parabolic variational inequality （VI） in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional nonlinear parabolic PDE containing a power penalty term with penalty constant λ〉 1 and a power parameter k 〉 0. We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order O（λ^-k/2）. A fitted finite volume method is designed to solve the nonlinear PDE, and some numerical experiments are performed to illustrate the usefulness of this method.展开更多
In this paper we derive some inequalities for traces and singular values of the quaternion matrices,extend and improve some of the corresponding results appeared in other papers we know.
To carry out the deep space exploration tasks near Sun-Earth Libration point L2, the CRTBP dynamic model was built up and the numerical conditional quasi-periodic orbit （Lissajons orbit） was computed near L2. Then, ...To carry out the deep space exploration tasks near Sun-Earth Libration point L2, the CRTBP dynamic model was built up and the numerical conditional quasi-periodic orbit （Lissajons orbit） was computed near L2. Then, a formation controller was designed with linear matrix inequality to overcome the difficuhy of parameter tuning. To meet the demands of formation accuracy and present thruster＇s capability, a threshold scheme was adopted for formation control. Finally, some numerical simulations and analysis were completed to demonstrate the feasibility of the proposed control strategy.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, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a cla...In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a class of prescribed σ2 curvature measure equations.展开更多
Abstract For relatively prime positive integers u0 and r, and for 0 〈 k ≤ n, define uk ：= u0 ＋ kr. Let Ln ：= 1cm（u0,u1,... ,un） and let a,l≥2 be any integers. In this paper, the authors show that, for integers...Abstract For relatively prime positive integers u0 and r, and for 0 〈 k ≤ n, define uk ：= u0 ＋ kr. Let Ln ：= 1cm（u0,u1,... ,un） and let a,l≥2 be any integers. In this paper, the authors show that, for integers α≥ a, r ≥max（a,l - 1） and n ≥lατ, the following inequality holds Ln≥u0r^（l-1）α＋a-l（r＋1）^n.Particularly, letting l = 3 yields an improvement on the best previous lower bound on Ln obtained by Hong and Kominers in 2010.展开更多
The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and g...The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and global asymptotic stability of posi- tive almost periodic solutions is obtained. Finally, an example and numerical simulations are performed for justifying the theoretical results.展开更多
This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensio...This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.展开更多
文摘Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.
文摘This paper aims to develop a power penalty method for a linear parabolic variational inequality （VI） in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional nonlinear parabolic PDE containing a power penalty term with penalty constant λ〉 1 and a power parameter k 〉 0. We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order O（λ^-k/2）. A fitted finite volume method is designed to solve the nonlinear PDE, and some numerical experiments are performed to illustrate the usefulness of this method.
文摘In this paper we derive some inequalities for traces and singular values of the quaternion matrices,extend and improve some of the corresponding results appeared in other papers we know.
文摘To carry out the deep space exploration tasks near Sun-Earth Libration point L2, the CRTBP dynamic model was built up and the numerical conditional quasi-periodic orbit （Lissajons orbit） was computed near L2. Then, a formation controller was designed with linear matrix inequality to overcome the difficuhy of parameter tuning. To meet the demands of formation accuracy and present thruster＇s capability, a threshold scheme was adopted for formation control. Finally, some numerical simulations and analysis were completed to demonstrate the feasibility of the proposed control strategy.
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.
文摘In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a class of prescribed σ2 curvature measure equations.
基金supported by the National Natural Science Foundation of China(No.10971145)the Ph.D.Programs Foundation of Ministry of Education of China(No.20100181110073)the Science&Technology Program of Sichuan Province(No.2013JY0125)
文摘Abstract For relatively prime positive integers u0 and r, and for 0 〈 k ≤ n, define uk ：= u0 ＋ kr. Let Ln ：= 1cm（u0,u1,... ,un） and let a,l≥2 be any integers. In this paper, the authors show that, for integers α≥ a, r ≥max（a,l - 1） and n ≥lατ, the following inequality holds Ln≥u0r^（l-1）α＋a-l（r＋1）^n.Particularly, letting l = 3 yields an improvement on the best previous lower bound on Ln obtained by Hong and Kominers in 2010.
文摘The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and global asymptotic stability of posi- tive almost periodic solutions is obtained. Finally, an example and numerical simulations are performed for justifying the theoretical results.
基金supported by the Science and Technology Foundation of Guizhou Province under Grant No.20102133
文摘This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.
