On Finding the Maximum Feasible Subsystem of a System of Linear Inequalities

被引：2
|
作者：
Katerinochkina N.N. [1 ]
Ryazanov V.V. [1 ]
Vinogradov A.P. [1 ]
Wang L. [2 ]
机构：
[1] Dorodnicyn Computing Centre of the Computer Science and Control Federal Research Center of the Russian Academy of Sciences, Moscow
[2] Nanjing University of Aeronautics and Astronautics, Nanjing
来源：
Pattern Recognition and Image Analysis | 2018年 / 28卷 / 2期
基金：
俄罗斯基础研究基金会;
关键词：
combinatorial algorithm; learning; linear inequality; logical regularity; optimization; precedent; relaxation; sigmoid function; system of inequalities;
D O I：
10.1134/S1054661818020104
中图分类号：
学科分类号：
摘要：
Some methods for finding the maximum feasible subsystems of systems of linear inequalities are considered. The problem of finding the most accurate algorithm in a parametric family of linear classification algorithms is one of the most important problems in machine learning. In order to solve this discrete optimization problem, an exact (combinatorial) algorithm, its approximations (relaxation and greedy combinatorial descent algorithms), and the approximation algorithm are given. The latter consists in replacing the original discrete optimization problem with a nonlinear programming problem by changing from linear inequalities to their sigmoid functions. The initial results of their comparison are presented. © 2018, Pleiades Publishing, Ltd.
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页码：169 / 173
页数：4
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