In this paper we consider three problems in continuous multi-criteria optimization: An application of the Berge Maximum Theorem, properties of Pareto-retract mappings, and the structure of Pareto sets. The key goal of...In this paper we consider three problems in continuous multi-criteria optimization: An application of the Berge Maximum Theorem, properties of Pareto-retract mappings, and the structure of Pareto sets. The key goal of this work is to present the relationship between the three problems mentioned above. First, applying the Maximum Theorem we construct the Pareto-retract mappings from the feasible domain onto the Pareto-optimal solutions set if the feasible domain is compact. Next, using these mappings we analyze the structure of the Pareto sets. Some basic topological properties of the Pareto solutions sets in the general case and in the convex case are also discussed.展开更多
This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class...This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of D （uk, un） and αtm,ln = 0 （（log log n）-（1＋ε））.展开更多
We give the sufficient conditions of Retaining Region Theorem and Maximum Modulus principle, The results of this paper are generatizations of rele rant results in [1,2].
This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both ...This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.展开更多
This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived vi...This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived via Duboviskij-Milujin theorem.展开更多
文摘In this paper we consider three problems in continuous multi-criteria optimization: An application of the Berge Maximum Theorem, properties of Pareto-retract mappings, and the structure of Pareto sets. The key goal of this work is to present the relationship between the three problems mentioned above. First, applying the Maximum Theorem we construct the Pareto-retract mappings from the feasible domain onto the Pareto-optimal solutions set if the feasible domain is compact. Next, using these mappings we analyze the structure of the Pareto sets. Some basic topological properties of the Pareto solutions sets in the general case and in the convex case are also discussed.
基金Project supported by the National Natural Science Foundation of China(11171275)the Natural Science Foundation Project of CQ(cstc2012jjA00029)Liaocheng University Foundation(X09005)
文摘This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of D （uk, un） and αtm,ln = 0 （（log log n）-（1＋ε））.
文摘We give the sufficient conditions of Retaining Region Theorem and Maximum Modulus principle, The results of this paper are generatizations of rele rant results in [1,2].
基金supported by the National Science Foundations (DMS0504783 DMS0604207)National Science Fund for Distinguished Young Scholars of China (70825005)
文摘This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.
文摘This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived via Duboviskij-Milujin theorem.
