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Mixed convexity and optimization results for functions with integer and real variables with applications to queueing systems.

机译：具有整数和实变量的函数的混合凸度和优化结果，以及在排队系统中的应用。

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摘要

In this dissertation, a new method for obtaining convexity and optimization results for functions with integer and real (i.e. mixed) variables is introduced and this new method is applied to obtain mixed convexity and optimization results for some of the known mixed variable functions in the literature. These mixed variable functions include the Erlang delay and loss formulae in telecommunication systems, an (S--1,S) inventory model (suggested by Das (1977)), and an M/ Ek/1 queueing system model (suggested by Kumin (1973)). Local and global mixed convexity and optimization results for these mixed variable functions are obtained after introducing definitions for a condense discrete convex set, a condense discrete convex function, a discrete Hessian matrix, a mixed convex set, a mixed convex function, and a mixed Hessian matrix. Symbolic toolbox of MATLAB R2009a is used to obtain symbolic results. Computational discrete and mixed convexity and optimization results are also obtained by using MATLAB R2009 a. The results obtained in this work are important because prior to this work no joint convexity results for mixed functions for mixed functions have been defined. This dissertation obtains such joint results. In addition, for real variable functions that are strictly convex, it is well-known that any local minimum is also the global minimum. In this work, similar results are obtained for mixed strictly convex functions. A new Hessian matrix defined for mixed variable functions can be used to determine whether any local minimum is also the global minimum.
机译：本文介绍了一种获取具有整数变量和实变量（即混合变量）的函数的凸性和最优化结果的新方法，并将这种新方法应用于文献中一些已知的混合变量函数的混合凸性和最优化结果。 。这些混合变量函数包括电信系统中的Erlang延迟和损耗公式，（S--1，S）库存模型（由Das（1977）建议）和M / Ek / 1排队系统模型（由Kumin（ 1973））。在引入了凝聚离散凸集，凝聚离散凸函数，离散Hessian矩阵，混合凸集，混合凸函数和混合Hessian的定义之后，获得了这些混合变量函数的局部和全局混合凸性以及优化结果。矩阵。 MATLAB R2009a的符号工具箱用于获取符号结果。使用MATLAB R2009 a还可以获得计算的离散凸凸和混合凸凸以及优化结果。在这项工作中获得的结果很重要，因为在此工作之前，尚未定义混合函数的混合函数的联合凸结果。本文获得了这样的联合结果。另外，对于严格凸的实变量函数，众所周知，任何局部最小值也是全局最小值。在这项工作中，对于混合严格凸函数也获得了相似的结果。为混合变量函数定义的新的Hessian矩阵可用于确定任何局部最小值是否也是全局最小值。

著录项

  • 作者

    Tokgoz, Emre.;

  • 作者单位

    The University of Oklahoma.;

  • 授予单位 The University of Oklahoma.;
  • 学科 Engineering Industrial.;Operations Research.
  • 学位 Ph.D.
  • 年度 2012
  • 页码 119 p.
  • 总页数 119
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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