Employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation for a class of stochastic differential d...Employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation for a class of stochastic differential delay equations with small noises, where the coefficients are allowed to be highly nonlinear growth with respect to the variables. Moreover, we obtain the central limit theorem for stochastic differential delay equations which the coefficients are polynomial growth with respect to the delay variables.展开更多
Based on the empirical or theoretical qualitative information about the relationship between response variable and covariates, we propose a new approach to model polynomial regression using a shape restricted regressi...Based on the empirical or theoretical qualitative information about the relationship between response variable and covariates, we propose a new approach to model polynomial regression using a shape restricted regression after estimating the direction by sufficient dimension reduction. The purpose of this paper is to illustrate that in the absence of prior information other than the shape constraints, our approach provides a flexible fit to the data and improves regression predictions. We use central subspace to estimate the directions and fit a final model by shape restricted regression, when the shape is known or is stipulated from empirical inspection. Comparisons with an alternative nonparametric regression are included. Simulated and real data analyses are conducted to illustrate the performance of our approach.展开更多
Interior-Point Methods(IPMs)not only are the most effective methods in practice but also have polynomial-time complexity.Many researchers have proposed IPMs for Linear Optimization(LO)and achieved plentiful results.In...Interior-Point Methods(IPMs)not only are the most effective methods in practice but also have polynomial-time complexity.Many researchers have proposed IPMs for Linear Optimization(LO)and achieved plentiful results.In many cases these methods were extendable for LO to Linear Complementarity Problems(LCPs)successfully.In this paper,motivated by the complexity results for linear optimization based on the study of H.Mansouri et al.(Mansouri and Zangiabadi in J.Optim.62(2):285–297,2013),we extend their idea for LO to LCP.The proposed algorithm requires two types of full-Newton steps are called,feasibility steps and(ordinary)centering steps,respectively.At each iteration both feasibility and optimality are reduced exactly at the same rate.In each iteration of the algorithm we use the largest possible barrier parameter valueθwhich lies between the two values 117n and 113n,this makes the algorithm faster convergent for problems having a strictly complementarity solution.展开更多
In this paper,a class of polynomial interior-point algorithms for P_(∗)(κ)-horizontal linear complementarity problems based on a newparametric kernel function is presented.The new parametric kernel function is used b...In this paper,a class of polynomial interior-point algorithms for P_(∗)(κ)-horizontal linear complementarity problems based on a newparametric kernel function is presented.The new parametric kernel function is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center of the problem.We derive the complexity analysis for the algorithm,both with large and small updates.展开更多
Africa is already experiencing the impact of climate change. Some of the manifestations of climate change in Africa are, changing weather patterns resulting in, flooding and drought. Temperature change has impacted he...Africa is already experiencing the impact of climate change. Some of the manifestations of climate change in Africa are, changing weather patterns resulting in, flooding and drought. Temperature change has impacted health, livelihoods, productivity of food, availability of water, and state of security. This study examines the long-term climate variations in Central African Countries (Gabon, Cameroon, Republic of Congo, Central Africa Republic, Chad and Democratic Republic of Congo) for the period 1901 to 2015, and then investigates the possible influence of increases in greenhouse gas concentrations. To investigate climate patterns and trends in the Central African Countries, precipitation and temperature were analyzed on annual time scales using data collected from the World Bank Group Climate Change Knowledge Portal. Data was further aggregated using annual average blocks of 10 years. Linear and polynomial regression was performed. Also, linear time series slopes were analyzed to investigate the spatial and temporal trends of climate variability in Central African countries. Results of the analyses indicated that the mean annual temperature and precipitation records in some of the Central African Countries had both warming and cooling trends over the study period from 1901 to 2015. For example, differences between the maximum and the minimum rainfall data for Democratic Republic of Congo, Cameroon and Gabon were 13 mm, 13 mm and 11.1 mm, which corresponded to 11.04%, 10.03% and 10.44% respectively. The study also found the temperature of Chad to have significantly risen from 1901 to 2015 by almost 20%, while its rainfall’s variation was limited. Although the variation in rainfall in Chad was not dramatic, the temperature per 10 year rose by almost 20%. Chad’s temperature rose according to a cubic model from about 24.5°C to just below 27°C during the period 1901-1940. This was followed by a brief drop between 1940 and 1960. From 1960 to 2015 it rose according to the model to almost 28°C. By 2040 the tempe展开更多
In this paper, we propose a general path following method, in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap. The algorithm...In this paper, we propose a general path following method, in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap. The algorithm maintains the O (nL) ineration complexity It enjoys quadratic convergence if the optimal vertex is nondegenerate.展开更多
基金The authors are grateful to the anonymous referees for their valuable comments and corrections. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11401592）, the Natural Science Foundation of Hunan Province （No. 13JJ5043）, and the Mathematics and Interdisciplinary Sciences Project of Central South University.
文摘Employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation for a class of stochastic differential delay equations with small noises, where the coefficients are allowed to be highly nonlinear growth with respect to the variables. Moreover, we obtain the central limit theorem for stochastic differential delay equations which the coefficients are polynomial growth with respect to the delay variables.
文摘Based on the empirical or theoretical qualitative information about the relationship between response variable and covariates, we propose a new approach to model polynomial regression using a shape restricted regression after estimating the direction by sufficient dimension reduction. The purpose of this paper is to illustrate that in the absence of prior information other than the shape constraints, our approach provides a flexible fit to the data and improves regression predictions. We use central subspace to estimate the directions and fit a final model by shape restricted regression, when the shape is known or is stipulated from empirical inspection. Comparisons with an alternative nonparametric regression are included. Simulated and real data analyses are conducted to illustrate the performance of our approach.
基金The authors are indebted to the referees for their careful reading of the manuscript and for their suggestions which helped to improve the paper.The authors also wish to thank Shahrekord University for financial support.
文摘Interior-Point Methods(IPMs)not only are the most effective methods in practice but also have polynomial-time complexity.Many researchers have proposed IPMs for Linear Optimization(LO)and achieved plentiful results.In many cases these methods were extendable for LO to Linear Complementarity Problems(LCPs)successfully.In this paper,motivated by the complexity results for linear optimization based on the study of H.Mansouri et al.(Mansouri and Zangiabadi in J.Optim.62(2):285–297,2013),we extend their idea for LO to LCP.The proposed algorithm requires two types of full-Newton steps are called,feasibility steps and(ordinary)centering steps,respectively.At each iteration both feasibility and optimality are reduced exactly at the same rate.In each iteration of the algorithm we use the largest possible barrier parameter valueθwhich lies between the two values 117n and 113n,this makes the algorithm faster convergent for problems having a strictly complementarity solution.
文摘In this paper,a class of polynomial interior-point algorithms for P_(∗)(κ)-horizontal linear complementarity problems based on a newparametric kernel function is presented.The new parametric kernel function is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center of the problem.We derive the complexity analysis for the algorithm,both with large and small updates.
文摘Africa is already experiencing the impact of climate change. Some of the manifestations of climate change in Africa are, changing weather patterns resulting in, flooding and drought. Temperature change has impacted health, livelihoods, productivity of food, availability of water, and state of security. This study examines the long-term climate variations in Central African Countries (Gabon, Cameroon, Republic of Congo, Central Africa Republic, Chad and Democratic Republic of Congo) for the period 1901 to 2015, and then investigates the possible influence of increases in greenhouse gas concentrations. To investigate climate patterns and trends in the Central African Countries, precipitation and temperature were analyzed on annual time scales using data collected from the World Bank Group Climate Change Knowledge Portal. Data was further aggregated using annual average blocks of 10 years. Linear and polynomial regression was performed. Also, linear time series slopes were analyzed to investigate the spatial and temporal trends of climate variability in Central African countries. Results of the analyses indicated that the mean annual temperature and precipitation records in some of the Central African Countries had both warming and cooling trends over the study period from 1901 to 2015. For example, differences between the maximum and the minimum rainfall data for Democratic Republic of Congo, Cameroon and Gabon were 13 mm, 13 mm and 11.1 mm, which corresponded to 11.04%, 10.03% and 10.44% respectively. The study also found the temperature of Chad to have significantly risen from 1901 to 2015 by almost 20%, while its rainfall’s variation was limited. Although the variation in rainfall in Chad was not dramatic, the temperature per 10 year rose by almost 20%. Chad’s temperature rose according to a cubic model from about 24.5°C to just below 27°C during the period 1901-1940. This was followed by a brief drop between 1940 and 1960. From 1960 to 2015 it rose according to the model to almost 28°C. By 2040 the tempe
文摘In this paper, we propose a general path following method, in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap. The algorithm maintains the O (nL) ineration complexity It enjoys quadratic convergence if the optimal vertex is nondegenerate.
