arXiv subjects

Samuel Awoniyi

Publications and source records attributed to Samuel Awoniyi.

6 recordsLinked to original sources

arXiv2025

A compact implementation of a recently proposed strongly polynomial-time algorithm for the general LP problem

This article presents a compact implementation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. Each iteration of the algorithm consists of applying a pair of complementary Gauss-Jordan (GJ) pivoting operations. In this compact implementation of the algorithm, the GJ pivoting operations are done inside a matrix that has half the size of the original matrix. A numerical illustration is given.

math.OC↗

arXiv2025

A strongly polynomial-time algorithm for the general linear programming problem

This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of linear equations constrained by complementarity relations and non-negative variables. Each iteration of the algorithm consists of applying a pair of complementary Gauss-Jordan pivoting operations, guided by a necessary-condition lemma. The algorithm requires no more than 2(k+n) iterations, as there are only k+n complementary pairs of columns to compare one-pair-at-a-time, where k is the number of constraints and n is the number of variables of given general linear programming problem. Numerical illustration is given that includes an instance of a classical problem of Klee and Minty and a problem of Beale.

math.OC↗

arXiv2024

On pairs of complementary GJ pivoting transforming skew-symmetric matrices

This article describes certain ratios that attend pairs of complementary Gauss-Jordan pivotings transforming skew-symmetric matrices. Our interest in those ratios was motivated by a need to prove a crucial Claim stated in a recently proposed strongly polynomial-time algorithm for the general LP problem. That Claim is proved in this article and, as a consequence of this proof, a compact implementation of the strongly polynomial-time algorithm is suggested.

math.OC↗

arXiv2023

Validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem

This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear programming problems into a special system of linear equations constrained by complementarity relations and non-negative variables. Each iteration of the algorithm consists of applying a pair of complementary Gauss-Jordan pivoting operations, guided by a necessary-condition lemma. This validation article demonstrates that the proposed algorithm requires no more than 2(k+n) iterations, where k is the number of constraints and n is the number of variables of given general linear programming problem.

math.OC↗

arXiv2023

Computation and applications of limits of certain non-stationary Markov chains

This article describes a method for computing limits of a class of non-stationary Markov chains motivated by healthcare sojourn-time cycles. A mathematical validation of the computation method is also given. Applications are described that include predicting cycles in healthcare and very large system maintenance. An objective of this article is to hopefully foster some investigation and teaching of practical non-stationary Markov chains.

math.PR↗

arXiv2023

A numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming problem

This article presents a numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming (LP) problem. This article is essentially the first half of an article that describes the proposed algorithm. Each iteration of the algorithm consists of two Gauss-Jordan pivoting operations. The algorithm is terminated after at most 2(k+n) iterations, where k is the number of constraints of the LP problem and n is the number of variables. Illustrative example LP problems described in this article include a Klee-Minty LP problem and an LP problem of Beale.

math.OC↗