Secant Update generalized version of PSB: a new approach

Nicolas Boutet (), Rob Haelterman and Joris Degroote
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Nicolas Boutet: Royal Military Academy
Rob Haelterman: Royal Military Academy
Joris Degroote: Ghent University

Computational Optimization and Applications, 2021, vol. 78, issue 3, No 10, 953-982

Abstract: Abstract In optimization, one of the main challenges of the widely used family of Quasi-Newton methods is to find an estimate of the Hessian matrix as close as possible to the real matrix. In this paper, we develop a new update formula for the estimate of the Hessian starting from the Powell-Symetric-Broyden (PSB) formula and adding pieces of information from the previous steps of the optimization path. This lead to a multisecant version of PSB, which we call generalised PSB (gPSB), but which does not exist in general as was proven before. We provide a novel interpretation of this non-existence. In addition, we provide a formula that satisfies the multisecant condition and is as close to symmetric as possible and vice versa for a second formula. Subsequently, we add enforcement of the last secant equation and present a comparison between the different methods.

Keywords: Non-linear optimization; Quasi-Newton formulae; Multisecant equations; Symmetric gradient; 90C53; 49M15 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-020-00256-1

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