An Efficient Version on a New Improved Method of Tangent Hyperbolas

摘要

An new inexact method of tangent hyperbolas (NIMTH) has been proposed recently. In NIMTH, the Newton equation and the Newton-like equation are solved respectively by one Cholesky factorization (CF) step and p preconditioned conjugate gradient (PCG) steps, periodically. The algorithm is efficient in theory. But its implementation is still restricted. In this paper, an efficient version of NIMTH is presented, in which the parameter p is independent of the complexity of the objective function, and its tensor terms can be efficiently evaluated by automatic differentiation. Further theoretical analysis and numerical experiments show that this version of NIMTH is of great competition for the middle and large scale unconstrained optimization problems.