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Variable metric bundle methods: From conceptual to implementable forms

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Abstract

To minimize a convex function, we combine Moreau-Yosida regularizations, quasi-Newton matrices and bundling mechanisms. First we develop conceptual forms using “reversal” quasi-Newton formulae and we state their global and local convergence. Then, to produce implementable versions, we incorporate a bundle strategy together with a “curve-search”. No convergence results are given for the implementable versions; however some numerical illustrations show their good behaviour even for large-scale problems.

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Authors and Affiliations

  1. INRIA, B.P. 105, 78153, Le Chesnay, France

    Claude Lemaréchal & Claudia Sagastizábal

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  1. Claude Lemaréchal
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  2. Claudia Sagastizábal
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Correspondence to Claude Lemaréchal.

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Lemaréchal, C., Sagastizábal, C. Variable metric bundle methods: From conceptual to implementable forms. Mathematical Programming 76, 393–410 (1997). https://doi.org/10.1007/BF02614390

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  • DOI: https://doi.org/10.1007/BF02614390

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