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曾金平
椭圆型算子变分不等式等非线性问题的数值解研究
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- 姓名：曾金平
- 目前身份：
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学术头衔：
博士生导师
- 职称：-
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学科领域：
计算数学
- 研究兴趣：椭圆型算子变分不等式等非线性问题的数值解研究
曾金平教授，自1986年于中科院计算中心硕士毕业后一直在湖南大学从事教研和科研工作。主讲多门本科生和研究生课程，培养硕士和博士研究生30余名。爱岗敬业，工作认真负责，教学效果好，曾获得湖南大学第二届青年教师讲课比赛一等奖、被列入原机械工业部首届跨世纪学术骨干培养计划和教育部优秀青年教师资助计划。博士论文被评为湖南省优秀博士学位论文。主编研究生教材《数值计算方法》及3本本科生教材，其中两本列入普通高等教育“十五”国家级规划教材。本人自硕士阶段起，开始并一直从事椭圆型算子变分不等式等非线性问题的数值解研究，先后在该领域主持并完成三项国家自然科学基金项目，目前主持国家自然科学基金一项、参加博士点专项基金一项（排名第二）。在相应问题的多重网格算法和区域分解算法以及多重分裂算法等数值解法的研究方面取得了一系列成果。共发表科研论文40余篇，其中被SCI、EI、ISTP三大检索收录30余次。部分成果被 “SIAM J. Numer. Anal.”、“ Numer. Math.”、“Math. Comput.”、“J. Optimz. Theory Appl.”等国际学术刊物多次引用。在指导的有关研究内容的硕士论文中，其中两篇获得湖南省优秀硕士学位论文。
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2005-07-06
【期刊论文】Geometric Convergence of Overlapping Schwarz Methods for Obstacle Problems
曾金平， Jinping Zeng
，-0001，（）：
-1年11月30日
A new catalyst system for the synthesis of R-aryl-substituted nitriles is reported. The bicyclic triaminophosphine P(i-BuNCH2CH2)3N (1b) serves as an efficient and versatile ligand for the palladium-catalyzed direct R-arylation of nitriles with aryl bromides. Using ligand 1b, ethyl cyanoacetate and primary as well as secondary nitriles are efficiently coupled with a wide variety of aryl bromides possessing electron-rich, electron-poor, electron-neutral, and sterically hindered groups.
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2005-07-06
【期刊论文】A domain decomposition method for a kind of optimization problems☆
曾金平， J.-P. Zeng *， S.Z. Zhou
Journal of Computational and Applied Mathematics 146(2002)127-139，-0001，（）：
-1年11月30日
In this paper, we are concerned with the monotone convergence of a multiplicative method for solving a kind of optimization problems. We showthat the iterate sequence produced by the method converges to the solution of the problem monotonically.
Optimization， Domain decomposition， Monotone convergence
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2005-07-06
【期刊论文】Monotonic Iterative Algorithms for an Implicit Two-Sided Obstacle Problem
曾金平， SHUZI ZHOU， JINPING ZENG AND WUPING ZHAN
Computers and Mathematics with Applications 43(2002)31-40，-0001，（）：
-1年11月30日
In this paper, we present some iterative algorithms, mainly Schwarz algorithms, for an implicit two-sided obstacle problem. The monotonic convergence of the algorithms is proved.
Two-sided obstacle problem,， Iterative algorithm,， Lower (， upper)， solution,， Schwarz algorithm,， Monotonic convergence.，
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2005-07-06
【期刊论文】Convergence of Broyden-Like Matrix
曾金平， DONGHUI LI， JINPING ZENG AND SHUZI ZHOU
Appl. Math. Lett. Vol. 11, No.5, pp. 35-37, 1998，-0001，（）：
-1年11月30日
n this paper, the convergence of Broyden-like matrices generated by Broyden-like method for solving nonlinear equations F(x) = 0 is discussed. Under suitable conditions, it is proved that the matrix sequence converges to the gradiauent of F(x).
nvergence,， Broyden-like matrix,， Nonlinear equations,， Nonlinear programming.，
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2005-07-06
曾金平， CHENLIANG LI*， JINPING ZENG AND SHUZI ZHOU
Computers and Mathematics with Applications 48(2004)373-386.，-0001，（）：
-1年11月30日
This paper proves the convergence of some generalized Schwarz algorithms for solving the obstacle problems with a T-monotone operator. Numerical results show that the generalized Sehwarz algorithms converge faster than the classical Schwarz algorithms.
Variational inequalities,， T-monotone operator,， Obstacle problems,， Convergence,， Generalized Schwarz algorithms.，
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2005-07-06
曾金平， Jin-Ping Zeng a， Dong-Hui Li a， Masao Fukushima b;*
Journal of Computational and Applied Mathematics 131(2001)1-14，-0001，（）：
-1年11月30日
In this paper, we consider an algebraic additive Schwarz iteration scheme for solving the 6nite-dimensional linear complementarity problem that involves an M-matrix. The scheme contains some existing algorithms as special cases. We establish monotone convergence of the iteration scheme under appropriate conditions. Moreover, using the concept of weak regular splitting, we estimate weighted max-norm bounds for iteration errors; thereby we show that the sequence generated by the iteration scheme converges to the unique solution of the problem without any restriction on the initial point.
Algebraic additive Schwarz iteration， Linear complementarity problem， Monotone convergence， Weighted max-norm
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2005-07-06
【期刊论文】Generalized Schwarz Algorithm for Obstacle Problems
曾金平， S. ZHOU， J. ZENG AND X. TANG
Computers and Mathematics with Applications 38(1999)263-271，-0001，（）：
-1年11月30日
this paper, we present so-called generalized additive and multiplicative Schwarz algorithms for solving the discretization problems of obstacle problems with a self-adjoint elliptic operator. We establish convergence theorems for the proposed algorithms. Numerical tests show that a faster convergence rate can be obtained by choosing suitable parameters in the algorithms.
Variational inequalities,， Obstacle problems,， Generalized Schwarz algorithms,， Con-vergence.，
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2005-07-06
【期刊论文】MONOTONIC ITERATIVE ALGORITHMS FOR A QUASICOMPLEMENTARITY PROBLEM*
曾金平， Shu-zi Zhou， Wu-ping Zan， Jin-ping Zeng
Journal of Computational Mathematics, Vol.19, No.3, 2001, 293-298.，-0001，（）：
-1年11月30日
We present two iterative algorithms, so called SCP and SA respectively, for soling quasicomplementarity problem (QCP). Algorithm SCP is to approximate QCP by a se-quence of ordinary complementarity problems(CP). SA is a Schwarz algorithm which can be implemented parllelly. We prove the algorithms above are monotonically convergent.
Quasicomplementarity problem,， Iterative algorthm,， Monotonic convergence,， Schwarz algorithm.，
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2005-07-06
【期刊论文】Block monotone iterative methods for elliptic variational inequalities ☆
曾金平， Jinping Zeng， Shuzi Zhou *
Applied Mathematics and Computation 128(2002)109-127，-0001，（）：
-1年11月30日
This paper discusses some important block iterative methods for solving variational inequalities with a nonlinear operator and proves their monotone convergence properties and comparison theorems.These results extend C.V.Pao’s research work in Numer.Math.(72) (1995) 239 to variational inequalities. _ 2002 Elsevier Science Inc. All rights reserved.
Monotone iterative scheme， Upper solution， Lower solution， Comparison theorem， Variational inequality
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2005-07-06
【期刊论文】Convergence Property of a Class of Variable Metric Methods
曾金平， ZHONG-ZHI ZHANG， Yiyang， Hunan， DING-HUA CAO AND JIN-PING ZENG*
Applied Mathematics Letters 17(2004)437-442，-0001，（）：
-1年11月30日
We investigate convergence property of the restricted Broyden class of variable metric methods. We show that when these methods with unit step are applied to a strictly convex quadratic objective function, the generated iterative sequence converges to the unique solution of the problem globally and superlinearly. Moreover, the distance between the iterative matrix and the Hessian matrix of the objective function decreases with iterations. The sequence of function vMues also exhibits descent property when the iteration is sufficiently large. (~) 2004 Elsevier Ltd. All rights reserved.
Variable metric methods,， Quadratic function.，
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