Efficient Algorithms for Large Optimization Problems

本研究的目的是开发有效的算法来解决大型优化问题，并探讨其理论特性和实际应用。2000年，我们为此做了基础研究。有三种类型的变量，自由变量，非负变量和有界变量。大型优化问题。我们研究了有效的算法，可以同时处理所有这些类型的变量。在2001年，我们研究了解决具有特殊结构的大型问题的算法。特别地，我们提出了一个求解多阶段随机规划问题的新算法。当级数不小时，这些问题可能非常大。我们使用的特殊结构的问题，并开发了一个有效的算法。在2002年，我们研究了一个新的算法来解决大型线性和非线性规划问题。该算法对问题中的变量进行对数变换。这种变换使得中心的路径平滑，算法高效。通过初步的计算实验，我们发现该算法可以非常快速地解决大型问题。

This research aims to develop efficient algorithms for solving large optimization problems and to investigate their theoretical properties and practical usage. In 2000, we did basic research for the purpose. There are 3 types of variables, free variables, nonnegative variables and bounded variables. in large optimization problems. We investigated efficient algorithms which can handle all these types of variables simultaneously. In 2001, we studied algorithms for solving large problems with a special structure. Especially, we proposed a new algorithm for solving multistage stochastic programming problems. These problems could be very large when the number of stages is not small. We use the special structure of the problems and developed an efficient algorithm for them. In 2002, we investigated a new algorithm for solving large linear and nonlinear programming problems. The algorithm uses a logarithmic transformation to the variables in the problem. This transformation makes the path of centers smooth and the algorithm efficient. From some preliminary computational experiment, we found that the algorithm can solve large problems very quickly.