Dyadic linear programming and extensions.

IF 2.5 2区 数学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Mathematical Programming Pub Date : 2025-01-01 Epub Date: 2024-10-03 DOI:10.1007/s10107-024-02146-4
Ahmad Abdi, Gérard Cornuéjols, Bertrand Guenin, Levent Tunçel
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引用次数: 0

Abstract

A rational number is dyadic if it has a finite binary representation p / 2 k , where p is an integer and k is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in floating-point arithmetic on a computer. A vector is dyadic if all its entries are dyadic rationals. We study the problem of finding a dyadic optimal solution to a linear program, if one exists. We show how to solve dyadic linear programs in polynomial time. We give bounds on the size of the support of a solution as well as on the size of the denominators. We identify properties that make the solution of dyadic linear programs possible: closure under addition and negation, and density, and we extend the algorithmic framework beyond the dyadic case.

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并矢线性规划及其扩展。
一个有理数是二进的,如果它有一个有限的二进制表示p / 2k,其中p是一个整数,k是一个非负整数。并进有理数对数值计算很重要,因为它们在计算机上的浮点运算中有精确的表示。如果一个向量的所有元素都是并进有理数,那么这个向量就是并进的。研究线性规划的二进最优解的求解问题。我们展示了如何在多项式时间内求解并矢线性规划。我们给出了一个解的支持的大小和分母的大小的界限。我们确定了使二元线性规划的解成为可能的性质:加法和负数下的闭包和密度,并且我们将算法框架扩展到二元情况之外。
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来源期刊
Mathematical Programming
Mathematical Programming 数学-计算机:软件工程
CiteScore
5.70
自引率
11.10%
发文量
160
审稿时长
4-8 weeks
期刊介绍: Mathematical Programming publishes original articles dealing with every aspect of mathematical optimization; that is, everything of direct or indirect use concerning the problem of optimizing a function of many variables, often subject to a set of constraints. This involves theoretical and computational issues as well as application studies. Included, along with the standard topics of linear, nonlinear, integer, conic, stochastic and combinatorial optimization, are techniques for formulating and applying mathematical programming models, convex, nonsmooth and variational analysis, the theory of polyhedra, variational inequalities, and control and game theory viewed from the perspective of mathematical programming.
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