A Note on the Existence of Nonsmooth Nonconvex Optimization Problems
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 49j 35q93