An $LDL^T$ Trust-Region Quasi-Newton Method

Johannes J Brust; Philip E Gill

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arXiv · 2312.06884

An $LDL^T$ Trust-Region Quasi-Newton Method

Johannes J Brust·Philip E Gill

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Abstract

For quasi-Newton methods in unconstrained minimization, it is valuable to develop methods that are robust, i.e., methods that converge on a large number of problems. Trust-region algorithms are often regarded to be more robust than line-search methods, however, because trust-region methods are computationally more expensive, the most popular quasi-Newton implementations use line-search methods. To fill this gap, we develop a trust-region method that updates an $LDL^T$ factorization, scales quadratically with the size of the problem, and is competitive with a conventional line-search method.

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BibTeX RIS

Johannes J Brust, Philip E Gill. 2023-12-11. An $LDL^T$ Trust-Region Quasi-Newton Method. https://arxiv.org/abs/2312.06884

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