A locally polynomial method for solving a system of linear inequalities-Reference-Cited by-同舟云学术

A locally polynomial method for solving a system of linear inequalities

Published:2021-06-01 Issue:2 Volume:50 Page:301-314
ISSN:2720-4278
Container-title:Control and Cybernetics
language:en
Short-container-title:

Author:

Evtushenko Yuri¹,Szkatuła Krzysztof²³,Tretyakov Alexey²³¹

Affiliation:

1. Dorodnicyn Computing Centre of FRC CSC, Russian Academy of Sciences Vavilov st. 40 , Moscow , Russia

2. Siedlce University of Natural Sciences and Humanities , Faculty of Science , ul. Konarskiego 2 , Siedlce , Poland

3. Systems Research Institute, Polish Academy of Sciences ul. Newelska 6 , Warszawa , Poland

Abstract

Abstract The paper proposes a method for solving systems of linear inequalities. This method determines in a finite number of iterations whether the given system of linear ineqalities has a solution. If it does, the solution for the given system of linear inequalities is provided. The computational complexity of the proposed method is locally polynomial.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/candc-2021-0015

Reference14 articles.

1. Evtushenko, Y. G. and Golikov, A. (2003) New perspective on the theorems of alternative. In: High Performance Algorithms and Software for Nonlinear Optimization, Springer, 227–241.10.1007/978-1-4613-0241-4_10

2. Facchinei, F., Fischer, A. and Kanzow, C. (1998) On the accurate identification of active constraints. SIAM Journal on Optimization, 9(1):14–32.10.1137/S1052623496305882

3. Goffin, J-L. (1982) On the non-polynomiality of the relaxation method for systems of linear inequalities. Mathematical Programming, 22(1):93–103.10.1007/BF01581028

4. Golikov, A. and Evtushenko, Y. G. (2003) Theorems of the alternative and their applications in numerical methods. Computational Mathematics and Mathematical Physics, 43(3):338–358.

5. Han, S-P. (1980) Least-squares solution of linear inequalities. Technical report, University of Wisconsin – Madison, Mathematical Research Center. November 1980.