A generalization of the norm-relaxed method of feasible directions

摘要

This paper generalizes the norm-relaxed method of feasible directions which has roots in the classical method of feasible directions (MFD). This generalized algorithm introduces some parameters which can be adjusted to speed up the convergence. An investigation of its global convergence is included and the numerical performance is shown on 15 test problems. Its global convergence is guaranteed under a rather mild and standard assumption. The numerical tests show that this new algorithm converges faster than the previous norm-relaxed MFD for most test problems by selecting a set of suitable parameters even though it only has the same guaranteed convergence rate as the previous norm-relaxed MFD.