A Randomised Subspace Gauss-Newton Method for Nonlinear Least-Squares

• URL: http://arxiv.org/abs/2211.05727v1
• Date: Thu, 10 Nov 2022 17:51:08 GMT
• Title: A Randomised Subspace Gauss-Newton Method for Nonlinear Least-Squares
• Authors: Coralia Cartis, Jaroslav Fowkes, Zhen Shao
• Abstract summary: We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems. A sublinear global rate of convergence result is presented for a trust-region variant of R-SGN, with high probability.
• Score: 0.6445605125467572
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on each iteration. A sublinear global rate of convergence result is presented for a trust-region variant of R-SGN, with high probability, which matches deterministic counterpart results in the order of the accuracy tolerance. Promising preliminary numerical results are presented for R-SGN on logistic regression and on nonlinear regression problems from the CUTEst collection.

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