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Piecewise linear approximations in nonconvex nonsmooth optimization

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Abstract

We present a bundle type method for minimizing nonconvex nondifferentiable functions of several variables. The algorithm is based on the construction of both a lower and an upper polyhedral approximation of the objective function. In particular, at each iteration, a search direction is computed by solving a quadratic program aiming at maximizing the difference between the lower and the upper model. A proximal approach is used to guarantee convergence to a stationary point under the hypothesis of weak semismoothness.

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Authors and Affiliations

  1. Dipartimento di Elettronica Informatica e Sistemistica, Università della Calabria, 87036, Rende (CS), Italy

    M. Gaudioso, E. Gorgone & M. F. Monaco

Authors
  1. M. Gaudioso
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  2. E. Gorgone
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  3. M. F. Monaco
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Corresponding author

Correspondence to M. Gaudioso.

Additional information

This research has been partially supported by the Italian “Ministero dell’Istruzione, dell’Università e della Ricerca”, under PRIN project Ottimizzazione Non Lineare e Applicazioni (20079PLLN7_003).

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Gaudioso, M., Gorgone, E. & Monaco, M.F. Piecewise linear approximations in nonconvex nonsmooth optimization. Numer. Math. 113, 73–88 (2009). https://doi.org/10.1007/s00211-009-0228-4

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Mathematics Subject Classification (2000)