Near boundary behavior of primal-dual potential reduction algorithms for linear programming
For a linear program of the form \(\min\{c^ T x;\;Ax=b,\;x\geq 0\}\) and the potential function \(\phi(x,s)=\rho_ P\ln(x^ T s)-\sum^ n_{j=1} \ln(x_ j s_ j)\), where \(s\) are dual slacks, the authors describe ranges (relative to \(\rho_ P\)) on the size of the parameter \(\rho_ s\) used in formulae for generating search directions which guarantee a constant reduction in the potential function.
scientific article; zbMATH DE number 221252
scientific article