DISCUSSION ON THE CONVERGENCE OF ROSEN''''S GRADIENT PROJECTION METHOD

Since Rosen's gradient projection method was published in 1960,a rigorous convergence proof ofthe method has remained to be an open question.A convergence proof for the three dimensional case isgiven in this paper.The whole proof,except one lemma which we failed to prove for the general case,is applicable to the general case.For the general case a convergence condition is given in the maintheorem.     

关于OR发展前途的讨论及其对OR应用工作的启示

本文介绍了自七十年代以来西方运筹学界对OR的本质和发展前途展开的讨论,并对其进行了初步的研究和综合分析,同时结合OR应用的机制、面临的问题以及应用的前途和机会等问题,对OR的应用进行了整体的分析和探讨,希望从中得到一点对我国OR应用工作的启示.     

改进的自组织映射(SOM)蛋白质折叠算法和计算实现

蛋白质结构预测是生物信息学中的重要研究方向．为了研究蛋白质折叠的机理,人们引入了只考虑蛋白质疏水核心和亲水外围位置导致能量差别的简化HP模型．即使是求解二维HP模型已被证明是一个NP完全问题,因此需要设计有效的近似算法来求解较大规模的HP模型．从旅行商问题(TSP)的求解看,自组织映射是构造近似算法的有效工具．本文将归一化的F-W自组织模型应用到蛋白质二维HP问题的求解中,结合为克服多重映射构造的局部线搜索算法．数值试验表明,该算法改进了现有的HP模型的SOM求解算法, 只需很少的迭代步数就能找到最低能量构象．这一改进算法可以成为进一步研究的基础．     

解线性不等式的神经网络

本文提出两个解线性不等式的Hopfiedl-Tank型的神经网络。第一个网络模拟同时松弛投影方法，第二个网络是二次规划方法。当线性不等式的解集非空时，这两个方法都给出该线性不等式的解。同时我们还给出了这两个网络的数值模拟。     

运筹学与管理信息系统的关系初探

本文的目的是通过对运筹学(Operations Research简称OR)和管理信息系统(Management Information Systems简称MIS)两者的历史发展的比较以及OR在MIS中已有的应用和可能起到的作用的讨论,来探讨OR和MIS这两个学科相结合的可能途径。这一问题近年来在国际上受到这两个学科的共同关心,就运筹学界来说,从H.J.Miser在1978年出版的《运筹学手册》里关于运筹学的历史、特点和应用的回顾,直到国际运筹学会     

An adaptive trust region method and its convergence

In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved. Numerical results indicate that the new method is very efficient.     

A trust-region and affine scaling algorithm for linearly constrained optimization

A new trust-region and affine scaling algorithm for linearly constrained optimization is presented in this paper. Under no nondegenerate assumption, we prove that any limit point of the sequence generated by the new algorithm satisfies the first order necessary condition and there exists at least one limit point of the sequence which satisfies the second order necessary condition. Some preliminary numerical experiments are reported. The work was done while visiting Institute of Applied Mathematics, AMSS, CAS.     

无约束优化的自适应信赖域方法

本文对无约束优化问题提出一个自适应信赖域方法,每次迭代都充分利用前迭代点的信息自动产生一个恰当的信赖域半径,在此区域内,二次模型与原目标函数尽可能一致,避免盲目的尝试,提高了计算效率。文中在通常条件下证明了全局收敛性及局部超线性收敛结果,给出了新算法与传统信赖域方法的数值结果,证实了新方法的有效性。     

Modified optimization layer by layer algorithm for learning multilayer perceptrons

1. IntroductionThe feedforward Multilayer Perceptron (MLP) is one of the most widely used artificial neural networks among other network models. Its field of application includes patternrecognition, identification and control of dynamic systems, system modeling and nonlinearprediction of time series, etc. [1--41 founded on its nonlinear function approximation capability. Research of this type of networks has been stimulated since the discovery andpopularization of the Backpropagation learnin…     

不等式约束最优化的非光滑精确罚函数的一个光滑近似

为不等式约束最优化问题提出一个连续可微近似罚函数并研究它的性质.在此基础上,提出了两个罚函数方法并证明这两个方法是全局收敛的.