An LDL^T Trust-Region Quasi-Newton Method

2023/12/11 by Johannes J. Brust, Philip E. Gill, Brust, Johannes J +1
Mathematics · Computer Science · #Advanced Optimization Algorithms Research #Matrix Theory and Algorithms #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.2312.06884

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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