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General Information
Prof. Adrian Olaru
University Politehnica of Bucharest, Romania
I'm happy to take on the position of editor in chief of IJMO. It's a journal that shows promise of becoming a recognized journal in the area of modelling and optimization. I'll work together with the editors to help it progress.
IJMO 2021 Vol.11(4): 107-111 ISSN: 2010-3697
DOI: 10.7763/IJMO.2021.V11.786

New Approach for Secant Update Generalized Version of PSB

N. Boutet, R. Haelterman, and J. Degroote
Abstract—Working with Quasi-Newton methods in optimization leads to one important challenge, being to find an estimate of the Hessian matrix as close as possible to the real matrix. While multisecant methods are regularly used to solve root finding problems, they have been little explored in optimization because the symmetry property of the Hessian matrix estimation is generally not compatible with the multisecant property. In this paper, we propose a solution to apply multisecant methods to optimization problems. Starting from the Powell-Symmetric-Broyden (PSB) update formula and adding pieces of information from the previous steps of the optimization path, we want to develop a new update formula for the estimate of the Hessian. A multisecant version of PSB is, however, generally mathematically impossible to build. For that reason, we provide a formula that satisfies the symmetry and is as close as possible to satisfy the multisecant condition and vice versa for a second formula. Subsequently, we add enforcement of the last secant equation to the symmetric formula and present a comparison between the different methods.

Index Terms—Non-linear, optimization, quasi-Newton formulas, multisecant equations, symmetric gradient.

N. Boutet and R. Haelterman are with Royal Military Academy, Brussels, and University Ghent, Belgium (e-mail: Nicolas.boutet@ugent.be).
J. Degroote is with University of Ghent, Belgium.


Cite: N. Boutet, R. Haelterman, and J. Degroote, "New Approach for Secant Update Generalized Version of PSB," International Journal of Modeling and Optimization vol. 11, no. 4, pp. 107-111, 2021.

Copyright © 2021 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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