An efficient version on a new improved method of tangent hyperbolas

Authors:
Haibin Zhang;Qiang Cheng;Yi Xue;Naiyang Deng
Affiliations:
College of Applied Science, Beijing University of Technology, Beijing, China;Supercomputing Center, CNIC, Chinese Academy of Sciences, Beijing, China;College of Applied Science, Beijing University of Technology, Beijing, China;College of Science, China Agricultural University, Beijing, China
Venue:
LSMS'07 Proceedings of the Life system modeling and simulation 2007 international conference on Bio-Inspired computational intelligence and applications
Year:
2007

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Abstract

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.