最优化理论在信息论中应用.docVIP

最优化理论在信息论中的应用 摘 要 关键词：ABSTRACT Optimization theory and algorithm is an important branch of mathmatics, which focus on how to measure various kinds of plans to pick out the best one as well as how to coming up with the most excellent plan. Such problems generally exist in most types of engineering calculation and design field, and the optimization provides a strong theoretical foundation and reliable algorithm for these solutions, which has played a huge role in the actual application. The information theory is based on the Shannons theorems and refers to a proportion of optimization problems on the information content and information capacity. In this paper, the application of optimization in the information theory field will be studied and analysed in the combination of part of the professional knowledge on the information and communication. With the help of Matlab numerical computation toolbox, the Zoutendijk feasible direction method in the optimization text concering on the problem with non-linear objective function and linear constrainted functions will be programmed to solve the corresponding problem of imformation theory. Through this process, the Shannons theorems can be explained in the aspect of numerical computation, which may gain the understanding of the theorems; and the optimization theory can be better grasped during the practical application. Keywords: optimization information theory Shannons theorems Feasible Direction Method Zoutendijk 1 引言 最优化方法是在给定约束之下，从问题的许多可能解答中，寻求使某一或某些指标达到最优解答，或者对于给定的问题通过何种途径去寻找最优解答的方法，它是一个重要的数学分支。 最优化是个古老的方法，早在17世纪从英国科学家牛顿提出极值问题开始，就已经出现了最优化研究的雏形。至20世纪40年代，由于生产和科学研究迅猛发展，尤其是电子计算机的广泛应用，一方面对最优化的研究有力空前的迫切需求，另一方面也为最优化研究提供了新型的有力的工具。最优化问题与现代电子技术结合，步入了全新发展的快车道，形成了一个新的学科，出现了线性规划、非线性规划、整数规划等众多的分支。 最优化问题普遍存在于各类工程设计和方案规划问题中，例如在工程设计中怎样选择设计参数，使设计方案既满足设计要求又能降低成本；在资源分配中，怎样分配有限资源，使得分配方案既能满足各方面的基本要求，又能获得好的经济效益。随着最优化学科的发展，及其与社会各领域的紧密结合，最优化理论和算法在实际中正发挥着越来越大的作用。 信息论是运用概率论与数理统计的方法研究信息、信息熵、通信系统、数据传输、密码学、数据压缩等问题的应用数学学科。狭义的信息论以香农信息论为基础，核心内