A method for solving the system of linear equations and linear inequalities

https://doi.org/10.1016/j.mcm.2006.12.007Get rights and content
Under an Elsevier user license
open archive

Abstract

A method, called the (I.) ABS-MPVT algorithm, for solving a system comprising linear equations and linear inequalities is presented. This method is characterized by solving the system of linear equations first via the ABS algorithms and then solving an unconstrained minimization obtained by substituting the ABS general form of solutions into the system of linear inequalities. For the unconstrained minimization problem it can be solved by a (modified) parallel algorithm. The convergence of this method is also given.

Keywords

ABS algorithms
Abaffian matrix
System of linear equations
System of linear inequalities
Parallel algorithm
Convex programming
Minimax
Nonlinear programming

Cited by (0)

This work was supported by the Natural Science Foundation of China, Grant 10471015 and the Natural Science Foundation of China, Grant 10671029.