In this paper, we introduce a new class of two-parametric penalized function,which includes the penalized minimum function and the penalized Fischer-Burmeister function over symmetric cone complementarity problems. We...In this paper, we introduce a new class of two-parametric penalized function,which includes the penalized minimum function and the penalized Fischer-Burmeister function over symmetric cone complementarity problems. We propose that this class of function is a class of complementarity functions(C-function). Moreover, its merit function has bounded level set under a weak condition.展开更多
This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming f...This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming from the same population but stored at different environments. The relevant algorithms are also provided. Simulation results manifest the soundness and effectiveness of the proposed model.展开更多
Using the axiomatic method, abstract concepts such as abstract mean, abstract convex function and abstract majorization are proposed. They are the generalizations of concepts of mean, convex function and majorization,...Using the axiomatic method, abstract concepts such as abstract mean, abstract convex function and abstract majorization are proposed. They are the generalizations of concepts of mean, convex function and majorization, respectively. Through the logical deduction, the fundamental theorems about abstract majorization inequalities are established as follows: for arbitrary abstract mean Σ and $ \Sigma ' $ and abstract ∑ ? $ \Sigma ' $ strict convex function f(x) on the interval I, if x i , y i ∈ I (i = 1, 2,..., n) satisfy that $ (x_1 ,x_2 , \ldots ,x_n ) \prec _n^\Sigma (y_1 ,y_2 , \ldots ,y_n ) $ then $ \Sigma ' $ {f(x 1), f(x 2),..., f(x n )} ? $ \Sigma ' $ {f(y 1), f(y 2),..., f(y n )}. This class of inequalities extends and generalizes the fundamental theorem of majorization inequalities. Moreover, concepts such as abstract vector mean are proposed, the fundamental theorems about abstract majorization inequalities are generalized to n-dimensional vector space. The fundamental theorem of majorization inequalities about the abstract vector mean are established as follows: for arbitrary symmetrical convex set $ \mathcal{S} \subset \mathbb{R}^n $ , and n-variable abstract symmetrical $ \overline \Sigma $ ? $ \Sigma ' $ strict convex function $ \phi (\bar x) $ on $ \mathcal{S} $ , if $ \bar x,\bar y \in \mathcal{S} $ , satisfy $ \bar x \prec _n^\Sigma \bar y $ , then $ \phi (\bar x) \geqslant \phi (\bar y) $ ; if vector group $ \bar x_i ,\bar y_i \in \mathcal{S}(i = 1,2, \ldots ,m) $ satisfy $ \{ \bar x_1 ,\bar x_2 , \ldots ,\bar x_m \} \prec _n^{\bar \Sigma } \{ \bar y_1 ,\bar y_2 , \ldots ,\bar y_m \} $ , then $ \Sigma '\{ \phi (\bar x_1 ),\phi (\bar x_2 ), \ldots ,\phi (\bar x_m )\} \geqslant \Sigma '\{ \phi (\bar y_1 ),\phi (\bar y_2 ), \ldots ,\phi (\bar y_m )\} $ .展开更多
文摘In this paper, we introduce a new class of two-parametric penalized function,which includes the penalized minimum function and the penalized Fischer-Burmeister function over symmetric cone complementarity problems. We propose that this class of function is a class of complementarity functions(C-function). Moreover, its merit function has bounded level set under a weak condition.
基金supported by the National Natural Science Foundation of P.R.China(60764003)the Major Project of The Ministry of Education of P.R.China and the Funded by Scientific Research Program of the HigherEducation Institution of Xinjiang(XJEDU2004I12 and XJEDU2006I05)
基金supported by National Natural Science Foundation of China (Grant No. 10571070)the China Postdoctoral Science Foundation (Grant No. 20060400514)
文摘This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming from the same population but stored at different environments. The relevant algorithms are also provided. Simulation results manifest the soundness and effectiveness of the proposed model.
基金supported by the National Key Basic Research Project of China (Grant No. 2004CB318003)the Foundation of the Education Department of Sichuan Province of China (Grant No. 07ZA087)
文摘Using the axiomatic method, abstract concepts such as abstract mean, abstract convex function and abstract majorization are proposed. They are the generalizations of concepts of mean, convex function and majorization, respectively. Through the logical deduction, the fundamental theorems about abstract majorization inequalities are established as follows: for arbitrary abstract mean Σ and $ \Sigma ' $ and abstract ∑ ? $ \Sigma ' $ strict convex function f(x) on the interval I, if x i , y i ∈ I (i = 1, 2,..., n) satisfy that $ (x_1 ,x_2 , \ldots ,x_n ) \prec _n^\Sigma (y_1 ,y_2 , \ldots ,y_n ) $ then $ \Sigma ' $ {f(x 1), f(x 2),..., f(x n )} ? $ \Sigma ' $ {f(y 1), f(y 2),..., f(y n )}. This class of inequalities extends and generalizes the fundamental theorem of majorization inequalities. Moreover, concepts such as abstract vector mean are proposed, the fundamental theorems about abstract majorization inequalities are generalized to n-dimensional vector space. The fundamental theorem of majorization inequalities about the abstract vector mean are established as follows: for arbitrary symmetrical convex set $ \mathcal{S} \subset \mathbb{R}^n $ , and n-variable abstract symmetrical $ \overline \Sigma $ ? $ \Sigma ' $ strict convex function $ \phi (\bar x) $ on $ \mathcal{S} $ , if $ \bar x,\bar y \in \mathcal{S} $ , satisfy $ \bar x \prec _n^\Sigma \bar y $ , then $ \phi (\bar x) \geqslant \phi (\bar y) $ ; if vector group $ \bar x_i ,\bar y_i \in \mathcal{S}(i = 1,2, \ldots ,m) $ satisfy $ \{ \bar x_1 ,\bar x_2 , \ldots ,\bar x_m \} \prec _n^{\bar \Sigma } \{ \bar y_1 ,\bar y_2 , \ldots ,\bar y_m \} $ , then $ \Sigma '\{ \phi (\bar x_1 ),\phi (\bar x_2 ), \ldots ,\phi (\bar x_m )\} \geqslant \Sigma '\{ \phi (\bar y_1 ),\phi (\bar y_2 ), \ldots ,\phi (\bar y_m )\} $ .
