摘要
Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.
Active set method and gradient projection method are currently the main approaches for linearly constrained convex programming. Interior-point method is one of the most effective choices for linear programming. In the paper a predictor-corrector interior-point algorithm for linearly constrained convex programming under the predictor-corrector motivation was proposed. In each iteration, the algorithm first performs a predictor-step to reduce the duality gap and then a corrector-step to keep the points close to the central trajectory. Computations in the algorithm only require that the initial iterate be nonnegative while feasibility or strict feasibility is not required. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The results show that the proposed algorithm is stable and robust.
基金
TheNationalNaturalScienceFoundationofChina(No.6 99740 43)
