Abstract
A QP-free, truncated hybrid (QPFTH) method was proposed and developed in [6] for solving sparse large-scale nonlinear programming problems. In the hybrid method, a truncated Newton method is combined with the method of multiplier. In every iteration level, either a truncated solution for a symmetric system of linear equations is determined by CG algorithm or an unconstrained subproblem is solved by the limited memory BFGS algorithm such that the hybrid algorithm is suitable to large0scale problems. In this paper, the consistency in the hybrid method and a steplength procedure are discussed and developed. The global convergence of QPFTH method is proved and the two-step Q-quadratic convergence rate is further analyzed.
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