Global Convergence Technique for the Newton Method with Periodic Hessian Evaluation

F. Lampariello and M. Sciandrone
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F. Lampariello: National Research Council
M. Sciandrone: National Research Council

Journal of Optimization Theory and Applications, 2001, vol. 111, issue 2, No 6, 358 pages

Abstract: Abstract The problem of globalizing the Newton method when the actual Hessian matrix is not used at every iteration is considered. A stabilization technique is studied that employs a new line search strategy for ensuring the global convergence under mild assumptions. Moreover, an implementable algorithmic scheme is proposed, where the evaluation of the second derivatives is conditioned to the behavior of the algorithm during the minimization process and the local convexity properties of the objective function. This is done in order to obtain a significant computational saving, while keeping acceptable the unavoidable degradation in convergence speed. The numerical results reported indicate that the method described may be employed advantageously in all applications where the computation of the Hessian matrix is highly time consuming.

Keywords: Unconstrained optimization; Newton-type methods; periodic Hessian evaluation; global and superlinear convergence; computational savings (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1011934418390

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