14 papers
Optimality conditions, approximate stationarity, and applications -- a story beyond Lipschitzness
Alexander Y. Kruger, Patrick Mehlitz
Approximate necessary optimality conditions in terms of Fréchet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective fun…
Subdifferentiation of nonconvex sparsity-promoting functionals on Lebesgue spaces
Patrick Mehlitz, Gerd Wachsmuth
Sparsity-promoting terms are incorporated into the objective functions of optimal control problems in order to ensure that optimal controls vanish on large parts of the underlying…
Asymptotic regularity for Lipschitzian nonlinear optimization problems with applications to complementarity-constrained and bilevel programming
Patrick Mehlitz
Asymptotic stationarity and regularity conditions turned out to be quite useful to study the qualitative properties of numerical solution methods for standard nonlinear and complem…
Calmness and Calculus: Two Basic Patterns
Matúš Benko, Patrick Mehlitz
We establish two types of estimates for generalized derivatives of set-valued mappings which carry the essence of two basic patterns observed troughout the pile of calculus rules.…
R-regularity of set-valued mappings under the relaxed constant positive linear dependence constraint qualification with applications to parametric and bilevel optimization
Patrick Mehlitz, Leonid I. Minchenko
The presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of stability analysis or bileve…
A note on partial calmness for bilevel optimization problems with linearly structured lower level
Patrick Mehlitz, Leonid I. Minchenko, Alain B. Zemkoho
Partial calmness is a celebrated but restrictive property of bilevel optimization problems whose presence opens a way to the derivation of Karush--Kuhn--Tucker-type necessary optim…