修乃华
非线性规划、变分不等式与互补问题、大范围优化、对策与决策、最优化技术在经济与交通等中的应用
个性化签名
- 姓名:修乃华
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学术头衔:
博士生导师, 教育部“新世纪优秀人才支持计划”入选者
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学科领域:
运筹学
- 研究兴趣:非线性规划、变分不等式与互补问题、大范围优化、对策与决策、最优化技术在经济与交通等中的应用
修乃华,男,1959年10月生于河北省临西县。1997年在中国科学院应用数学研究所获得博士学位,现为北京交通大学教授、博士生导师。研究领域:运筹学、最优化方法及其应用。先后撰写著作一部;编写研究生教材一本;发表论文50余篇,其中SCI检索论文28篇。代表性论文刊登在该领域中较有影响的国际杂志《SIAM J. Optimization》、《Math. Programming》、《Numer. Math.》、《Appl. Math.Optim.》、《J.Global Optim.》、《J.Optim. Theory Appl.》等上。论文涉及该领域内的多个研究方向:非线性规划、变分不等式与互补问题、大范围优化、对策与决策、最优化技术在经济与交通等中的应用。特别是对变分不等式与互补问题的研究取得了重要成果:与美国华盛顿州立大学陈滨桐教授合作首次提出一个求解互补问题的具有大范围线性与局部二次收敛性的非内点连续法;证明了变分不等式问题的投影类型法具有最优面/解有限步识别性质;证得了GLP梯度投影法求解凸规划问题所产生的迭代点列具有全收敛性。全部论文累计被SCI引用100余次;一篇论文被美国ISI公司确认为 “高影响力论文”;某些研究成果被有关专著引述。近五年来,他在北京交通大学完成了三项国家或省部级基金项目。正在主持两项国家自然科学基金项目和一项教育部重点基金项目。正在参与香港城市大学研究基金资助项目,并到香港城市大学作为研究员(Research Fellow)工作累计近2年。曾获得过中科院院长奖学金优秀奖、中科院亿利达奖和第五届北京青年优秀论文个人奖。2004年获得教育部“新世纪优秀人才”。
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修乃华, B. CHEN, AND N. XIU
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 108, No. 2, pp. 317~332, FEBRUARY 2001,-0001,():
-1年11月30日
We propose a noninterior continuation method for the monotone linear complementarity problem (LCP) by modifying the Burke-Xu framework of the noninterior predictor-corrector path-following method (Refs. 1-2). The new method solves one system of linear equations and carries out only one line search at each iteration. It is shown to converge to the LCP solution globally linearly and locally superlinearly without the assumption of strict complementarity at the solution. Our analysis of the continuation method is based on a broader class of the smooth functions introduced by Chen and Mangasarian (Ref. 3).
Linear complementarity problems,, noninterior continuation methods,, linear and superlinear convergence.,
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修乃华, N. Xiu, , C. Wang, and J. Zhang
Appl Math Optim 43: 147~168 (2001),-0001,():
-1年11月30日
In this paper we develop the convergence theory of a general class of projection and contraction algorithms (PC method), where an extended stepsize rule is used, for solving variational inequality (VI) problems. It is shown that, by defining a scaled projection residue, the PC method forces the sequence of the residues to zero. It is also shown that, by defining a projected function, the PC method forces the sequence of projected functions to zero. A consequence of this result is that if the PC method converges to a nondegenerate solution of the VI problem, then after a finite number of iterations, the optimal face is identified. Finally, we study local convergence behavior of the extragradient algorithm for solving the KKT system of the inequality constrained VI problem.
Variational inequality,, Projection and contraction method,, Predictorcorrector stepsize,, Convergence property.,
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【期刊论文】Global s-type error bound for the extended linear complementarity problem and applications
修乃华, Jianzhong Zhang, Naihua Xiu
Mathematics Subject Classification (1991): 90C30, 90C33,-0001,():
-1年11月30日
For the extended linear complementarity problem over an affine subspace, we first study some characterizations of (strong) column/row monotonicity and (strong) R0-property. We then establish global s-type error bound for this problem with the column monotonicity or R0-property, especially for the one with the nondegeneracy and column monotonicity, and give several equivalent formulations of such error bound without the square root term for monotone affine variational inequality. Finally, we use this error bound to derive some properties of the iterative sequence produced by smoothing methods for solving such a problem under suitable assumptions.
the extended linear complementarity problem-monotonicity-R0-property-global s-type error bound
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【期刊论文】Local Convergence Analysis of Projection-Type Algorithms: Unified Approach1
修乃华, N. H. XIU, AND J. Z. ZHANG
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 115, No.1, pp. 211~230, October 2002 (2002),-0001,():
-1年11月30日
In this paper, we use a unified approach to analyze the local convergence behavior of a wide class of projection-type methods for solving variational inequality problems. Under certain conditions, it is shown that, in a finite number of iterations, either the sequence of iterates terminates at a solution of the concerned problem or all iterates enter and remain in the relative interior of the optimal face and, hence, the subproblem reduces to a simpler form.
Variational inequalities,, projection methods,, local convergence.,
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【期刊论文】Identification of the Optimal Active Set in a Noninterior Continuation Method for LCP
修乃华, NAIHUA XIU, and JIANZHONG ZHANG
Journal of Global Optimization 26: 183~198, 2003.,-0001,():
-1年11月30日
This paper concerns about the possibility of identifying the active set in a noninterior continuation method for solving the standard linear complementarity problem based on the algorithm and theory presented by Burke and Xu (J. Optim. Theory Appl. 112 (2002) 53). It is shown that under the assumptions of P-matrix and nondegeneracy, the algorithm requires at most O (ρ log (β0μ0/τ)) iterations to find the optimal active set, where β0 is the width of the neighborhood which depends on the initial point, μ0 > 0 is the initial smoothing parameter, ρ is a positive number which depends on the problem and the initial point, and τ is a small positive number which depends only on the problem.
Linear complementarity,, P-matrix,, Noninterior continuation method,, Optimal active set
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【期刊论文】Some recent advances in projection-type methods for variational inequalities
修乃华, Naihua Xiua, Jianzhong Zhangb, *
Journal of Computational and Applied Mathematics 152(2003)559~585,-0001,():
-1年11月30日
Projection-type methods are a class of simple methods for solving variational inequalities, especially for complementarity problems.In this paper we review and summarize recent developments in this class of methods, and focus mainly on some new trends in projection-type methods.
Variational inequality problem, Complementarity problem, Projection method, Predictor, Corrector
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【期刊论文】Convergence of the Gradient Projection Method for Generalized Convex Minimization*
修乃华, CHANGYU WANG, NAIHUA XIU
Computational Optimization and Applications, 16, 111~120, 2000,-0001,():
-1年11月30日
This paper develops convergence theory of the gradient projection method by Calamai andMore (Math. Programming, vol. 39, 93-116, 1987) which, for minimizing a continuously differentiable optimization problem min{f .(x): x ∈ Ω} where Ω is a nonempty closed convex set, generates a sequence xk+1=(ak-ak)▽f (xk))where the stepsize ak > 0 is chosen suitably. It is shown that, when f (x) is a pseudo-convex (quasi-convex) function, this method has strong convergence results: either xk→x* and x* is a minimizer (stationary point); or ‖xk‖→arg min{f (x) : x ∈ Ω}= and f (xk) inf{ f (x): x ∈ Ω}.
generalized convex minimization,, gradient projection method,, global convergence
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修乃华, BINTONG CHEN†, AND NAIHUA XIU‡
SIAM J. OPTIM. 1999 Society for Industrial and Applied Mathematics Vol. 9, No.3, pp. 605~623,-0001,():
-1年11月30日
A noninterior continuation method is proposed for nonlinear complementarity problems. It improves the noninterior continuation methods recently studied by Burke and Xu [Math. Oper. Res., 23 (1998), pp. 719{734} and Xu [The Global Linear Convergence of an Infeasible Non-Interior Path-following Algorithm for Complementarity Problems with Uniform P-functions, Preprint, Department of Mathematics, University of Washington, Seattle, 1996]; the interior point neighborhood technique is extended to a broader class of smoothing functions introduced by Chen and Mangasarian [Comput. Optim. Appl., 5 (1996), pp. 97{138}. The method is shown to be globally linearly convergent following the methodology established by Burke and Xu. In addition, a local acceleration step is added to the method so that it is also locally quadratically convergent under suitable assumptions.
nonlinear complementarity problem,, continuation method,, smoothing function,, global linear convergence,, local quadratic convergence
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【期刊论文】Modified Fixed-Point Equations and Related Iterative Methods for Variational Inequalities
修乃华, NAIHUA XIU, YiJu WANG, XIANGSUN ZHANG
Computers and Mathematics with Applications 47(2004)913~920,-0001,():
-1年11月30日
In this paper, we study the equivalence characterizations of several modified fixedpoint equations to variational inequalities (VI). Based on these equations, we give some applications in constructing iterative methods for the solution of the VI. Especially, we show global convergence, the sublinear convergence, and the finite termination of a new iterative algorithm under certain conditions.
Variational inequalities,, Fixed-point equation,, Projection,, lterative method.,
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【期刊论文】A Characteristic Quantity of P-Matrices
修乃华, NAIHUA XIu, JIANZHONG ZHANG
Applied Mathematics Letters 15(2002)41~46,-0001,():
-1年11月30日
In this note, we develop some new properties of a fundamental quantity associated with a P-matrix introduced by Mathias and Pang[1]. Also, based on extensions of such a quantity, we obtain global error bounds for the vertical and horizontal linear complementarity problems.
P-matrix,, Vertical (, horizontal), linear complementarity problem,, Global error bound.,
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