A Note on the Existence of Nonsmooth Nonconvex Optimization Problems
- 577 Downloads
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.
KeywordsNonsmooth 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”.