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A CLASS OF NONMONOTONE SPECTRAL MEMORY GRADIENT METHOD
Zhensheng Yu,Jinsong Zang,Jingzhao Liu 대한수학회 2010 대한수학회지 Vol.47 No.1
In this paper, we develop a nonmonotone spectral memory gradient method for unconstrained optimization, where the spectral stepsize and a class of memory gradient direction are combined efficiently. The global convergence is obtained by using a nonmonotone line search strategy and the numerical tests are also given to show the efficiency of the proposed algorithm.
Empirical likelihood-based inference in varying-coefficient single-index models
Zhensheng Huang 한국통계학회 2011 Journal of the Korean Statistical Society Vol.40 No.2
This article deals with statistical inferences based on varying-coefficient parts in varying-coefficient single-index models (VCSIM). To improve the accuracy of the normal approximation-based confidence regions/intervals, an estimated empirical likelihoodbased statistic is proposed. The resulting statistic is shown to be asymptotically chisquared distributed. The construction of the empirical likelihood-based confidence regions of some varying-coefficient components in VCSIM is considered. In addition, the pointwise confidence intervals for a single function of the varying-coefficient parts are constructed. A simulation study is carried out to compare our results with several existing methods.
Empirical likelihood for single-index varying-coefficient models with right-censored data
Zhensheng Huang 한국통계학회 2010 Journal of the Korean Statistical Society Vol.39 No.4
This paper is concerned with an estimation procedure of a class of single-index varyingcoefficient models with right-censored data. An adjusted empirical log-likelihood ratio for the index parameters, which are of primary interest, is proposed using a synthetic data approach. The adjusted empirical likelihood is shown to have a standard chi-squared limiting distribution. Furthermore, we increase the accuracy of the proposed confidence regions by using the constraint that the index is of norm 1. Simulation studies are carried out to highlight the performance of the proposed method compared with the traditional normal approximation method.
Zhensheng Fu,Xiangyi Hu,Jianhua Zhang 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.1
Ye’s nonlinear cumulative damage model has been widely used in engineering because of its simple mathematical form and clear physical meaning. However, it does not consider the interaction between two different loads, so its prediction accuracy has large room for improvement. In this paper, the k-th power of load ratio is introduced into Ye’s model to reflect the influence of the interaction between two different loads on fatigue damage during the damage evolution process, and a generalized expression of the model is obtained. Based on this generalized expression, a new fatigue life prediction method is proposed. The proposed method is validated by comparison with existing versions based on the experimental data of typical engineering materials under two-level and multilevel loads. The results show that the prediction method proposed here can well reflect the load interaction effect, and compared with other models, this method has a more accurate prediction effect on the fatigue life of four materials.
TESTS FOR VARYING-COEFFICIENT PARTS ON VARYING-COEFFICIENT SINGLE-INDEX MODEL
Zhensheng Huang,Riquan Zhang 대한수학회 2010 대한수학회지 Vol.47 No.2
To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the Â2-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.
Combining trust region and linesearch algorithm for equality constrained optimization
Zhensheng Yu,Changyu Wang,Jiguo Yu 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.14 No.-
In this paper, a combining trust region and line search algorithm for equality constrained optimization is proposed. At each iteration, we only need to solve the trust region subproblem once, when the trust region trial step can not be accepted, we switch to line search to obtain the next iteration. Hence, the difficulty of repeated solving trust region subproblem in an iterate is avoided. In order to allow the direction of negative curvature, we add second correction step in trust region step and employ nonmonotone technique in line search. The global convergence and local superlinearly rate are established under certain assumptions. Some numerical examples are given to illustrate the efficiency of the proposed algorithm.
On the global convergence of a Levenberg-Marquardt method for constrained nonlinear equations
Zhensheng Yu 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
In this paper, we consider a Levenberg-Marquardt method for the solution of constrained nonlinear equation problems. The global convergence is established even without requiring the existence of an accumulation point. Some numerical tests are also presented.
COMBINING TRUST REGION AND LINESEARCH ALGORITHM FOR EQUALITY CONSTRAINED OPTIMIZATION
Yu, Zhensheng,Wang, Changyu,Yu, Jiguo 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.14 No.1
In this paper, a combining trust region and line search algorithm for equality constrained optimization is proposed. At each iteration, we only need to solve the trust region subproblem once, when the trust region trial step can not be accepted, we switch to line search to obtain the next iteration. Hence, the difficulty of repeated solving trust region subproblem in an iterate is avoided. In order to allow the direction of negative curvature, we add second correction step in trust region step and employ nonmonotone technique in line search. The global convergence and local superlinearly rate are established under certain assumptions. Some numerical examples are given to illustrate the efficiency of the proposed algorithm.
TESTS FOR VARYING-COEFFICIENT PARTS ON VARYING-COEFFICIENT SINGLE-INDEX MODEL
Huang, Zhensheng,Zhang, Riquan Korean Mathematical Society 2010 대한수학회지 Vol.47 No.2
To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the $\chi^2$-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.
ON THE GLOBAL CONVERGENCE OF A LEVENBERG-MARQUARDT METHOD FOR CONSTRAINED NONLINEAR EQUATIONS
Yu, Zhensheng 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.1
In this paper, we consider a Levenberg-Marquardt method for the solution of constrained nonlinear equation problems. The global convergence is established even without requiring the existence of an accumulation point. Some numerical tests are also presented.