Linearized Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Domain

The alternating direction method of multipliers (ADMM) for separable convex optimization of real functions in complex variables has been proposed recently[21]. Furthermore, the convergence and $O(1/K)$ convergence rate of ADMM in complex domain have also been derived[22]. In this paper, a fast linearized ADMM in complex domain has been presented as the subproblems do not have closed solutions. First, some useful results in complex domain are developed by using the Wirtinger Calculus technique. Second, the convergence of the linearized ADMM in complex domain based on the VI is established. Third, an extended model of least absolute shrinkage and selectionator operator (LASSO) is solved by using linearized ADMM in complex domain. Finally, some numerical simulations are provided to show that linearized ADMM in complex domain has the rapid speed.     

Income distribution dependence of poverty measure: A theoretical analysis

Using a modified deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the ‘global’ mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reduction in poverty while an increase in the variance of the income distribution increases poverty. This altruistic view for a developing economy, however, is not tenable anymore once the poverty index is found to follow a pareto distribution. Here although a rising mean income indicates a reduction in poverty, due to the presence of an inflexion point in the poverty function, there is a critical value of the variance below which poverty decreases with increasing variance while beyond this value, poverty undergoes a steep increase followed by a decrease with respect to higher variance. Identifying this inflexion point as the poverty line, we show that the pareto poverty function satisfies all three standard axioms of a poverty index [N.C. Kakwani, Econometrica 43 (1980) 437; A.K. Sen, Econometrica 44 (1976) 219] whereas the log-normal distribution falls short of this requisite. Following these results, we make quantitative predictions to correlate a developing with a developed economy.     

一类二阶非线性奇摄动边值问题解的渐近展开

本文研究一类非线性微分方程的非线性边值问题的奇摄动,应用边界层校正法构造出解的形式渐近展开式,并借助于上,下解及微分不等式理论研究解及其一阶导数的有关余项估计。     

一类非散度型椭圆方程的正则性

本文得到了一类带奇异低阶项椭圆万程的非负解的Harnack不等式、方程的形式为L0u+biuxi=0,其中L0为一具Holder连续系数的非散度型椭圆算子,|b|2属于Kato类.     

Quadratically and superlinearly convergent algorithms for the solution of inequality constrained minimization problems

In this paper, some Newton and quasi-Newton algorithms for the solution of inequality constrained minimization problems are considered. All the algorithms described produce sequences {x _k } convergingq-superlinearly to the solution. Furthermore, under mild assumptions, aq-quadratic convergence rate inx is also attained. Other features of these algorithms are that only the solution of linear systems of equations is required at each iteration and that the strict complementarity assumption is never invoked. First, the superlinear or quadratic convergence rate of a Newton-like algorithm is proved. Then, a simpler version of this algorithm is studied, and it is shown that it is superlinearly convergent. Finally, quasi-Newton versions of the previous algorithms are considered and, provided the sequence defined by the algorithms converges, a characterization of superlinear convergence extending the result of Boggs, Tolle, and Wang is given.This research was supported by the National Research Program Metodi di Ottimizzazione per la Decisioni, MURST, Roma, Italy.     

A SSLE-Type Algorithm of Quasi-Strongly Sub-Feasible Directions for Inequality Constrained Minimax Problems

In this paper, we discuss the nonlinear minimax problems with inequality constraints. Based on the stationary conditions of the discussed problems, we propose a sequential systems of linear equations (SSLE)-type algorithm of quasi-strongly sub-feasible directions with an arbitrary initial iteration point. By means of the new working set, we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix of the system of linear equations (SLE). At each iteration, two systems of linear equations (SLEs) with the same uniformly nonsingular coefficient matrix are solved. Under mild conditions, the proposed algorithm possesses global and strong convergence. Finally, some preliminary numerical experiments are reported.     

高密度情形格点Sierpinski地毯上渗流模型无穷开串的唯一性

本文证明高密度情形格点Ｓｉｅｒｐｉｎｓｋｉ地毯上边渗流模型无穷开串的唯一性,同时给出本模型相变存在性的一个新的证明．一种再标度技巧被发展并用作我们证明的主要工具．     

半正定Hermitian矩阵的广义Schur补的Lner偏序和特征值

首先得到了半正定 Hermitian矩阵的方幂的广义 Schur补的 L owner偏序的一些结果 ,然后改进了半正定 Hermitian矩阵的 Schur补的交错不等式 .     

关于一般Hilbert二重级数定理的改进

应用Ｅｌｕｅｒ求和公式．证明对任意正整数ｎ及实数ｐ＞１．有这里，由此改进了一般Ｈｉｌｂｅｒｔ二重级数定理．