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An inexact proximal regularization method for unconstrained optimization

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Abstract

We present a regularization algorithm to solve a smooth unconstrained minimization problem.This algorithm is suitable to solve a degenerate problem, when the Hessian is singular at a local optimal solution. The main feature of our algorithm is that it uses an outer/inner iteration scheme. We show that the algorithm has a strong global convergence property under mild assumptions. A local convergence analysis shows that the algorithm is superlinearly convergent under a local error bound condition. Some numerical experiments are reported.

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Authors and Affiliations

  1. Faculté des Sciences et Techniques, XLIM Laboratory – University of Limoges, 123, Avenue Albert Thomas, 87060, Limoges, France

    Paul Armand & Isaï Lankoandé

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  1. Paul Armand
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  2. Isaï Lankoandé
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Correspondence to Paul Armand.

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Armand, P., Lankoandé, I. An inexact proximal regularization method for unconstrained optimization. Math Meth Oper Res 85, 43–59 (2017). https://doi.org/10.1007/s00186-016-0561-1

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  • DOI: https://doi.org/10.1007/s00186-016-0561-1

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