缓冲和约简多维分布函数及其在优化中的应用

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters Pub Date : 2023-10-09 DOI:10.1007/s11590-023-02045-1

Bogdan Grechuk, Michael Zabarankin, Alexander Mafusalov, Stan Uryasev

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引用次数: 1

摘要

对于随机变量，超分布已经成为一个有价值的概率概念。与累积分布函数(CDF)类似，它唯一地定义了随机变量，并且可以用简单的一维最小化公式进行计算。本工作利用该公式的结构为随机向量引入缓冲CDF (bCDF)和减少CDF (rCDF)。证明bCDF和rCDF分别是多元CDF的最小schur -凸上界和最大schur -凹下界。利用bCDF和rCDF的特殊结构，构造了一种求解目标约束下bCDF和rCDF优化问题的算法。以约束条件下具有bCDF函数的债务抵押债券优化为例，验证了该算法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Buffered and Reduced Multidimensional Distribution Functions and Their Application in Optimization

Abstract For a random variable, superdistribution has emerged as a valuable probability concept. Similar to cumulative distribution function (CDF), it uniquely defines the random variable and can be evaluated with a simple one-dimensional minimization formula. This work leverages the structure of that formula to introduce buffered CDF (bCDF) and reduced CDF (rCDF) for random vectors. bCDF and rCDF are shown to be the minimal Schur-convex upper bound and the maximal Schur-concave lower bound of the multivariate CDF, respectively. Special structure of bCDF and rCDF is used to construct an algorithm for solving optimization problems with bCDF and rCDF in objective or constraints. The efficiency of the algorithm is demonstrated in a case study on optimization of a collateralized debt obligation with bCDF functions in constraints.

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来源期刊

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.