On large-scale unconstrained optimization and arbitrary regularization

J. M. Martínez () and L. T. Santos ()
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J. M. Martínez: IMECC–UNICAMP, University of Campinas
L. T. Santos: IMECC–UNICAMP, University of Campinas

Computational Optimization and Applications, 2022, vol. 81, issue 1, No 1, 30 pages

Abstract: Abstract We present a new algorithm for large-scale unconstrained minimization that, at each iteration, minimizes, approximately, a quadratic model of the objective function plus a regularization term, not necessarily based on a norm. We prove convergence assuming only gradient continuity and complexity results assuming Lipschitz conditions. For solving the subproblems in the case of regularizations based on the 3-norm, we introduce a new method that quickly obtains the approximate solutions required by the theory. We present numerical experiments.

Keywords: Smooth unconstrained minimization; Regularization; Newton-type methods (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-021-00322-2

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