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Journal of Systems Science & Complexity 2010年第4期23卷 861-872页

作者： Liying LIU Zengxin WEI Xiaoping WU College of Mathematics Science Liaocheng University Liaocheng 252059 China College of Mathematics and Information Science Guangxi University Nanning 530004 China School of Management Xi'an Jiaotong University Xi'an 710049 China

In this paper,a new modified BFGS method without line searches is *** traditionalBFGS method,this modified BFGS method is proposed based on the so-called fixed steplengthstrategy introduced by Sun and *** some suitable assumptions,the global convergence andthe superlinear convergence of the new algorithm are established,*** some preliminarynumerical experiments,which shows that the new Algorithm is feasible,is also reported.

关键词： BFGS method complexity systems global convergence superlinear convergence unconstrained optimization.

A New Subdivision Algorithm for the Bernstein Polynomial Approach to Global optimization

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International Journal of Automation and computing 2007年第4期4卷 342-352页

作者： P.S.V.Nataraj M.Arounassalame Systems and Control Engineering ACRE BuildingIndian Institute of Technology BombayPowaiMumbai 400076India

In this paper, an improved algorithm is proposed for unconstrained global optimization.to tackle non-convex nonlinear multivariate polynomial programming problems. The proposed algorithm is based on the Bernstein polynomial approach. Novel features of the proposed algorithm are that it uses a new rule for the selection of the subdivision point, modified rules for the selection of the subdivision direction, and a new acceleration device to avoid some unnecessary subdivisions. The performance of the proposed algorithm is numerically tested on a collection of 16 test problems. The results of the tests show the proposed algorithm to be superior to the existing Bernstein algorithm in terms of the chosen performance metrics.

关键词： Bernstein polynomials global optimization nonlinear optimization polynomial optimization unconstrained optimization.

ON THE CONVERGENCE OF A NEW HYBRID PROJECTION ALGORITHM

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Journal of Systems Science & Complexity 2006年第3期19卷 423-430页

作者： Qian LIU Changyu WANG Xinmin YANG Department of Mathematics Inner Mongolia University Hohhot 010021 China. Institute of Operations Research Qufu Normal University Qufu 273165 China. Department of Mathematics Chongqing Normal University Chongqing 400047 China Department of Mathematics Inner Mongolia University Hohhot 010021 China.

For unconstrained optimization. a new hybrid projection algorithm is presented m the paper. This algorithm has some attractive convergence properties. Convergence theory can be obtained under the condition that Δ↓f（x） is uniformly continuous. If Δ↓f（x） is continuously differentiable pseudo-convex, the whole sequence of iterates converges to a solution of the problem without any other assumptions. Furthermore, under appropriate conditions one shows that the sequence of iterates has a cluster-point if and only if Ω＊ ≠ θ. Numerical examples are given at the end of this paper.

关键词： Global convergence hybrid projection unconstrained optimization.

A CLASSOF NONMONOTONE CONJUGATE GRADIENT METHODSFOR NONCONVEX FUNCTIONS

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Applied Mathematics(A Journal of Chinese Universities) 2002年第2期17卷 208-214页

作者： LiuYun WeiZengxin Dept.ofMath. YunanUniv.Kunming650091China Dept.ofMath.andInform.Sci. GuangxiUniv.Nanning530004China

This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object *** class of methods includes the nonmonotone counterpart of modified Polak- Ribiè... 详细信息

关键词： nonmonotone conjugate gradient method,nonmonotone line search,global convergence unconstrained optimization.