Iterative method for solving the linear feasibility problem
Consider the linear feasibility problem of finding a solution \(x^*\) of a consistent system of linear inequalities \(G^Tx\leq b,\) where \(G\) is a matrix of size \(n\times m\) with columns \( g_{i}\in \mathbb R^n\), \(i\in I=\{ 1,\dots ,m\}\), \(x=(x_1,x_2\dots,x_n)^T\in \mathbb R^n\), \(b=(b_1,b_2,\dots ,b_m)^T\in \mathbb R^m\). Some solution methods use relaxed, averaged projections and other invoke surrogate constraints as for example Yang-Murty' method [\textit{K. Yang} and \textit{K. G. Murty}, J. Optim. Theory Appl. 72, 163--185 (1992; Zbl 0793.90035)]. In this paper the author proposes (Iterative Scheme 2.1) a blend of these two approaches. The author compares the computation results of his method with the surrogate constraint method of Yang-Murty and points out the advantage of his method.
scientific article; zbMATH DE number 5346077