ON A DUAL CHARACTERIZATION OF THE ASYMPTOTIC CONE FOR THE SOLUTION SET OF A LINEAR OPTIMIZATION PROBLEM
By
J. N. Singh1, M. Shakil2 and D. Singh3
1Department of Mathematics and Computer Science, Barry University, Miami Shores, Florida, USA-33161
2Department of Mathematics, Miami-Dade College, Hialeah, FL, USA-33012
3Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
Email: jsingh@barry.edu, mshakil@mdc.edu,mathdss@yahoo.com
(Received: July 13, 2023; In format : August 26, 2023; Revised : November 26, 2023; Accepted : November 28, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53215
Abstract
The concept of the asymptotic cone is very useful in various branches of pure and applied mathematics, especially in optimization and variational inequalities. In recent years, many authors and researchers have studied asymptotic directions and asymptotically convergent algorithms for unbounded solution sets. In this paper, we consider the asymptotic cone of the solution set Ω of a linear optimization problem and investigate various results on its asymptotic cone, asymptotic regularity, the dual and polar cones of the asymptotic cone, the support function of the solution set, etc. Finally, we present a dual characterization of the asymptotic cone Ω∞ for the solution set of a linear optimization problem.
2020 Mathematical Sciences Classification: 90C05, 90C60, 46B06, 40A05.
Keywords and Phrases: Linear optimization, Asymptotic cones, Asymptotic regularity, Normalized set, Positive hull, Polar cone, Dual cone, Support function.