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A Note on the Existence of Nonsmooth Nonconvex Optimization Problems

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Abstract

Sufficient conditions for the existence of a solution to an abstract optimization problem in Banach spaces are given, which do not rely on convexity, regularity properties or a straightforward coerciveness assumption. Applications to sparsity-constrained optimization and to problems from mechanics are provided.

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References

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Acknowledgments

K. Ito research partially supported by US-ARO grant 49308-MA and US-AFSOR grant FA 9550-06-1-0241. K. Kunisch supported in part by the Fonds zur Förderung der wissenschaftlichen Forschung under SFB 32, “Mathematical Optimization and Applications in the Biomedical Sciences”.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC , 27695-8205, USA

    Kazufumi Ito

  2. Institut für Mathematik, Karl-Franzens-Universität Graz, 8010 , Graz, Austria

    Karl Kunisch

Authors
  1. Kazufumi Ito
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  2. Karl Kunisch
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Correspondence to Karl Kunisch.

Additional information

Communicated by Giuseppe Buttazzo.

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Ito, K., Kunisch, K. A Note on the Existence of Nonsmooth Nonconvex Optimization Problems. J Optim Theory Appl 163, 697–706 (2014). https://doi.org/10.1007/s10957-014-0552-4

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  • DOI: https://doi.org/10.1007/s10957-014-0552-4

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