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A new infeasible proximal bundle algorithm for nonsmooth nonconvex constrained optimization

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Abstract

Proximal bundle method has usually been presented for unconstrained convex optimization problems. In this paper, we develop an infeasible proximal bundle method for nonsmooth nonconvex constrained optimization problems. Using the improvement function we transform the problem into an unconstrained one and then we build a cutting plane model. The resulting algorithm allows effective control of the size of quadratic programming subproblems via the aggregation techniques. The novelty in our approach is that the objective and constraint functions can be any arbitrary (regular) locally Lipschitz functions. In addition the global convergence, starting from any point, is proved in the sense that every accumulation point of the iterative sequence is stationary for the improvement function. At the end, some encouraging numerical results with a MATLAB implementation are also reported.

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Acknowledgements

The second-named author was partially supported by a Grant from IPM (No. 98900417). The authors would like to extend gratitude toward the anonymous referees whose suggestions helped to improve the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Isfahan, Isfahan, Iran

    Najmeh Hoseini Monjezi & S. Nobakhtian

  2. Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    S. Nobakhtian

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  1. Najmeh Hoseini Monjezi
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  2. S. Nobakhtian
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Correspondence to S. Nobakhtian.

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Hoseini Monjezi, N., Nobakhtian, S. A new infeasible proximal bundle algorithm for nonsmooth nonconvex constrained optimization. Comput Optim Appl 74, 443–480 (2019). https://doi.org/10.1007/s10589-019-00115-8

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