SOME REMARKS ON THE ASYMPTOTIC BEHAVIOR OF THE SOLUTION SET IN LINEAR OPTIMIZATION
By
J. N. Singh*1 , M. Shakil2 and D. Singh3
*1Department of Mathematics and Computer Science, Barry University, Miami Shores, Florida 33161, USA
2Department of Mathematics, Miami-Dade College, Hialeah, FL 33012, USA
3Department of Mathematics, Ahmadu Bello University Zaria, Nigeria
Email:jsingh@barry.edu, mshakil@mdc.edu and mathdss@yahoo.com
(Received : August 15, 2021 ; In format : August 22, 2021 ; Revised in final form : October 12, 2021)
DOI: https://doi.org/10.58250/Jnanabha.2021.51216
Abstract
In this paper, we investigate some results to characterize the unboundedness of the solution set in a linear optimization problem using an asymptotic cone, asymptotic regularity, normalized set, and positive hull of the solution set. The results of the Bolzano-Weierstrass theorem on the convergence in a finite-dimensional Euclidean space Rn have been frequently used to prove various propositions for linear optimization.
2020 Mathematical Sciences Classification: 90C05, 90C60, 46B06, 40A05
Keywords and Phrases: Linear optimization, Asymptotic cones, Asymptotic regularity, Normalized set, Positive hull, Unbounded sequence, Bolzano-Weierstrass theorem.