Journal of Optimization Theory and Applications

, Volume 163, Issue 3, pp 697–706 | Cite as

A Note on the Existence of Nonsmooth Nonconvex Optimization Problems

  • Kazufumi Ito
  • Karl KunischEmail author


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.


Nonsmooth Nonconvex optimization Coerciveness 

Mathematics Subject Classification (2000)

49J 35Q93 



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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.Institut für MathematikKarl-Franzens-Universität GrazGrazAustria

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