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.
The work was supported by the Mathematics and Physics Foundation of Beijing University of Technology (Grant No.Kz0603200381) and the National Science Foundation of China (Grant No.60503031).
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Zhang, H., Cheng, Q., Xue, Y., Deng, N. (2007). An Efficient Version on a New Improved Method of Tangent Hyperbolas. In: Li, K., Fei, M., Irwin, G.W., Ma, S. (eds) Bio-Inspired Computational Intelligence and Applications. LSMS 2007. Lecture Notes in Computer Science, vol 4688. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74769-7_23
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DOI: https://doi.org/10.1007/978-3-540-74769-7_23
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