Theoretical efficiency of a shifted-barrier-function algorithm for linear programming
The author gives an algorithm for solving a linear program \(\min \{C^ Tx| \quad Ax=b,\quad x\geq 0\},\) using a sequence of shifted-barrier problems \(\min \{C^ Tx-\epsilon \cdot \sum^{n}_{j=1}\ln (x_ j+\epsilon h_ j)| \quad Ax=b,\quad x+\epsilon h>0\}\) for a fixed shift vector \(h>0\), and a sequence of \(\epsilon >0\), that converges to zero. The advantages of the shifted-barrier algorithm are presented.
scientific article; zbMATH DE number 4205884