30 citations · 92 across the 38 of their papers we have counts for
5 papers · 1 filter
Convergence Properties of Monotone and Nonmonotone Proximal Gradient Methods Revisited
Christian Kanzow, Patrick Mehlitz
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradie…
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…
An Augmented Lagrangian Method for Optimization Problems with Structured Geometric Constraints
Xiaoxi Jia, Christian Kanzow, Patrick Mehlitz +1
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifi…
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…