离散集上的精确惩罚方法

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2022-05-01 DOI:10.1016/j.disopt.2021.100622

Nicolò Gusmeroli , Angelika Wiegele

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引用次数: 8

摘要

我们解决了在二元变量的线性约束下最小化二次函数的问题。引入了一种精确求解方法——EXPEDIS，将约束问题转化为最大切实例，然后利用最大切可用的全部机械来求解转化后的问题。我们推导理论是为了寻找一种精神上的转化，一种精确的刑罚方法;然而，我们只对二元变量集合的精确性感兴趣。为了计算最大切割，我们使用求解器BiqMac。数值结果表明，该算法可以成功地应用于各种类型的问题。

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EXPEDIS: An exact penalty method over discrete sets

We address the problem of minimizing a quadratic function subject to linear constraints over binary variables. We introduce the exact solution method called EXPEDIS where the constrained problem is transformed into a max-cut instance, and then the whole machinery available for max-cut can be used to solve the transformed problem. We derive the theory in order to find a transformation in the spirit of an exact penalty method; however, we are only interested in exactness over the set of binary variables. In order to compute the maximum cut we use the solver BiqMac. Numerical results show that this algorithm can be successfully applied on various classes of problems.

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.