The authors discuss interior-point methods for linear programming derived by applying a logarithmic barrier transformation and performing projected Newton steps for a sequence of barrier parameters. Under certain conditions, one of these projected Newton barrier methods is shown to be equivalent to Karmarkar's (1984) projective method for linear programming. Details are given of a specific barrier algorithm and its practical implementation. Numerical results are given for several nontrivial test problems. Additional keywords: tables(data); numerical analysis; iterations; computations; least squares method. (Author)