一类熵型的内邻近点算法及其应用

The Type of Entropy-like Interior Proximal Point Algorithms with the Applications

作者: 专业:运筹学与控制论 导师:董云达 年度:2010 学位:硕士  院校: 郑州大学

Keywords

Interior proximal point algorithm, Entropy-like distance function, Logarithmic-quadratic proximal point algorithm, Subdifferential, Convergence, Variational inequality

        我们在这篇文章中考虑在非负约束下的一类凸规划问题,并研究了两种内邻近点类型的算法。这些算法主要是通过用某个特殊的非线性距离函数来取代一般的二次邻近项,并且保证了产生的点总是内点。它们也可以应用于求解变分不等式问题和单调包含问题。本文由三部分组成,具体分布如下:在第一章中,我们简要的介绍了内邻近点算法的背景及其研究进展情况,并给出了一些基本概念和记号。第二章我们主要在熵型一阶齐次距离函数的基础之上添加了一般的邻近点项,通过参数的不同选取,使得目标函数有更快的下降速度,并在多面体约束下进行了相应的推广。针对熵型距离函数的特点,我们给出了解集的一个重要性质。第三章我们基于熵型二阶齐次距离函数在非负约束下得到了一些收敛性结果,并且给出了一些实际应用的例子加以分析说明。
    We in this thesis consider a class of convex programming problems subjected to nonnegative constraints, and study two types of interior proximal methods.These methods depend on some particular nonlinear distance function that replaces the usual quadratic proximal term,and the resulting points are always interior points.They can be applied to variational inequalities and monotone inclusions.This thesis consists of three chapters, and is organized as follow:In the first chapter,we briefly introduce the background of interior proximal point algorithm and its research progress,and gives some basic concepts and notation. In the second chapter, we add to the usual quadratic proximal point term on the based of an entropy-like first order homogeneous distance function,through selecting the different parameters to make the objective function has a faster decent rate, and extend to the polyhedra. By the characteristics of entropy-like distance function, we give an important property of the solution set. In the third chapter,we obtain some convergence results of an entropy-like second order homogeneous distance function that subjected to nonnegative constraints,and we give some examples of practical applications to further analysis.
        

一类熵型的内邻近点算法及其应用

摘要4-5
Abstract5
第一章 绪论7-12
    1.1引言7-10
    1.2.预备知识10-12
第二章 关于熵型一阶齐次距离函数的内邻近点方法的进一步研究12-28
    2.1 非负约束下的内邻近点方法12-23
    2.2 熵型内邻近点算法的应用推广23-28
第三章 关于熵型二阶齐次距离函数的内邻近点方法的进一步研究28-36
    3.1 非负约束下的内邻近点方法28-34
    3.2 熵型内邻近点算法的实例分析34-36
参考文献36-39
后记39-40
附录 硕士期间主要研究成果40-41
致谢41
        下载全文需10


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