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首页> 外文学位 >ALGORITHMIC PROBLEMS IN FACTORABLE PROGRAMMING WITH APPLICATION TO SOLUTION OF A NONLINEAR PROGRAMMING PROBLEM IN SYSTEMS DYNAMICS.
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ALGORITHMIC PROBLEMS IN FACTORABLE PROGRAMMING WITH APPLICATION TO SOLUTION OF A NONLINEAR PROGRAMMING PROBLEM IN SYSTEMS DYNAMICS.

机译：可分解程序设计中的算法问题，用于解决系统动力学中的非线性程序设计问题。

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摘要

This work is concerned with algorithmic and computational problems that arise when a computer code based on the Sequential Unconstrained Minimization Technique and factorable functions is used to solve a nonlinear programming problem in systems dynamics.; The usual representation of the dynamic optimization problem in factorable form requires a large number of repetitive blocks of input files. An indexing capability, paralleling that used by the FORTRAN compiler, is developed to reduce the size of the input and facilitate the user representation of the dynamic model.; The dynamic structure of the model gives rise to an inordinate number of dyads to represent the Hessian matrices. A procedure to reduce the number of outer product forms that requires little computational effort is developed. This allows the efficient solution of the model using Newton's method.; An indirect method is devised to allow sensitivity and elasticity analysis in situations in which the parameters of the problem are dependent on an underlying set of parameters.; An algorithm based on cubic and quartic approximations to the step-size problem is developed. This speeds convergence and also allows for satisfactory resolution of the difficulties associated with using directions of nonpositive curvature of the step-size function in a modified Newton method. The radius and rate of convergence of this algorithm are analyzed in detail.
机译：这项工作涉及当使用基于顺序无约束最小化技术和可分解函数的计算机代码来解决系统动力学中的非线性编程问题时出现的算法和计算问题。动态优化问题通常以可分解形式表示，需要输入文件的大量重复块。开发了与FORTRAN编译器并行的索引功能，以减少输入的大小并简化动态模型的用户表示。该模型的动态结构产生了无数倍数来表示黑森州矩阵。开发了一种减少外部产品形式数量的程序，所需的计算量很少。这样就可以使用牛顿法对模型进行有效的求解。设计了一种间接方法，可以在问题的参数依赖于基础参数集的情况下进行敏感性和弹性分析。提出了一种基于三次和四次逼近步长问题的算法。这加快了收敛速度，还可以令人满意地解决与在改进的牛顿法中使用步长函数的非正曲率方向有关的困难。详细分析了该算法的半径和收敛速度。

著录项

  • 作者

    NASSER, AHMED AWAD ABD EL-FATAH.;

  • 作者单位

    The George Washington University.;

  • 授予单位 The George Washington University.;
  • 学科 Operations Research.
  • 学位 D.Sc.
  • 年度 1985
  • 页码 208 p.
  • 总页数 208
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 运筹学;
  • 关键词

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