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.

引用

页码：169 / 173

页数：4

共 50 条

[31] Finding maximum linear subsystems of nonlinear systems with outputs
Xu, Z
Hunt, LR
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2000, 45 (09) : 1701 - 1704
[32] Maximum feasibility problem for continuous linear inequalities with applications to fuzzy linear programming
Jan, G.M.
Sheu, R.L.
Wu, S.Y.
Fuzzy Optimization and Decision Making, 2003, Kluwer Academic/Plenum Publishers (02) : 297 - 316
[33] FINDING FUGACITY FEASIBLE
MACKAY, D
ENVIRONMENTAL SCIENCE & TECHNOLOGY, 1979, 13 (10) : 1218 - 1223
[34] FEASIBILITY DETERMINATION WHEN THE FEASIBLE REGION IS DEFINED BY NON-LINEAR INEQUALITIES
Solow, Daniel
Szechtman, Roberto
Yucesan, Enver
2020 WINTER SIMULATION CONFERENCE (WSC), 2020, : 2800 - 2811
[35] Optimisation of two variables function with linear inequalities constraints - Contraction of the feasible region
Ammar, H
Cherruault, Y
KYBERNETES, 2000, 29 (9-10) : 1272 - 1283
[36] Finding a feasible schedule on a tree-connected processor system
Kawaguchi, Tsuyoshi, 1600, (20):
[37] NEW EFFICIENT ALGORITHM FOR FINDING A FEASIBLE POINT TO NON-LINEAR CONSTRAINTS
GARCIA, U
RESTUCCIA, A
ACTA CIENTIFICA VENEZOLANA, 1978, 29 : 30 - 30
[38] MAXIMUM FEASIBLE MANIPULATION
ARNSTEIN, SR
PUBLIC ADMINISTRATION REVIEW, 1972, 32 (SEP) : 377 - 390
[39] A method for solving the system of linear equations and linear inequalities
Pang, Li-Ping
Spedicato, Emilio
Xia, Zun-Quan
Wang, Wei
MATHEMATICAL AND COMPUTER MODELLING, 2007, 46 (5-6) : 823 - 836
[40] A SYSTEM OF LINEAR INEQUALITIES WITH INEXACT COEFFICIENTS
RAMIK, J
RIMANEK, J
EKONOMICKO-MATEMATICKY OBZOR, 1983, 19 (04): : 412 - 426

← 1 2 3 4 5 →