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Spectral bundle methods for non-convex maximum eigenvalue functions: second-order methods

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Abstract

We study constrained and unconstrained optimization programs for nonconvex maximum eigenvalue functions. We show how second order techniques may be introduced as soon as it is possible to reliably guess the multiplicity of the maximum eigenvalue at a limit point. We examine in which way standard and projected Newton steps may be combined with a nonsmooth first-order method to obtain a globally convergent algorithm with a fair chance to local superlinear or quadratic convergence.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse, France

    Dominikus Noll

  2. Control System Department, CERT-ONERA, 2, avenue Edouard Bélin, 31055, Toulouse, France

    Pierre Apkarian

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  1. Dominikus Noll
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  2. Pierre Apkarian
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Correspondence to Dominikus Noll.

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Dedicated to R. T. Rockafellar on the occasion of his 70th anniversary

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Noll, D., Apkarian, P. Spectral bundle methods for non-convex maximum eigenvalue functions: second-order methods. Math. Program. 104, 729–747 (2005). https://doi.org/10.1007/s10107-005-0635-y

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  • DOI: https://doi.org/10.1007/s10107-005-0635-y

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