30 citations · 43 across the 28 of their papers we have counts for
6 papers · 2 filters
On implicit variables in optimization theory
Matúš Benko, Patrick Mehlitz
Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several differe…
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.…
Asymptotic stationarity and regularity for nonsmooth optimization problems
Patrick Mehlitz
Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional as…
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…
Reformulation of the M-stationarity conditions as a system of discontinuous equations and its solution by a semismooth Newton method
Felix Harder, Patrick Mehlitz, Gerd Wachsmuth
We show that the Mordukhovich-stationarity system associated with a mathematical program with complementarity constraints (MPCC) can be equivalently written as a system of disconti…