MODIFIED PARTIAL-UPDATE NEWTON-TYPE ALGORITHMS FOR UNARY OPTIMIZATION

In this paper, we propose two modified partial-update algorithms for s olving unconstrained unary optimization problems based on trust-region stabilization via indefinite dogleg curves. The two algorithms partia lly update an approximation to the Hessian matrix in each iteration by utilizing a number of times the rank-one updating of the Bunch-Parlet t factorization. In contrast with the original algorithms in Ref. 1, t he two algorithms not only converge globally, but possess also a local ly quadratic or superlinear convergence rate. Furthermore, our numeric al experiments show that the new algorithms outperform the trust-regio n method which uses the partial update criteria suggested in Ref. 1.