NONMONOTONE PRECONDITIONAL CURVILINEAR PATH ALGORITHMS FOR UNCONSTRAINED OPTIMIZATION

摘要

This paper presents nonmonotonic quasi-Newton algorithms via two pre-conditional curvilinear paths, the preconditional modified gradient path and the precon-ditional optimal path, for unconstrained optimization problem. We employ the stableBunch-Parlett factorization method to form two curvilinear paths very easily. Thenonmonotone criterion is used to speed up the convergence progress in the contoursof objective function with large curvature. Theoretical analyses are given which provethat the proposed algorithms are globally convergent and have a local superlinear con-vergence rate under some reasonable conditions. The results of numerical experimentsare reported to show the effectiveness of the proposed algorithms.