30 citations · 92 across the 38 of their papers we have counts for
42 papers
A penalty-type method for relaxed inverse optimal control problems
Floriane Mefo Kue, Patrick Mehlitz, Thorsten Raasch
This paper is devoted to the introduction and analysis of a penalty-type method for the numerical treatment of a class of bilevel optimization problems arising from inverse optimal…
Elastically safeguarded augmented Lagrangian methods
Ernesto G. Birgin, Alberto De Marchi, Patrick Mehlitz
We investigate, theoretically and numerically, a class of elastically safeguarded augmented Lagrangian methods for nonlinear optimization problems with inequality and equality cons…
On directional local minimality and directional optimality conditions in nonsmooth optimization
Timm Baake, Patrick Mehlitz
This paper considers the unconstrained minimization of a lower semicontinuous function. Exploiting first and second subderivatives, directional limiting subdifferentials, and direc…
Uniqueness and stability of Lagrange multipliers and associated qualification conditions
Patrick Mehlitz, Gerd Wachsmuth
This paper is concerned with uniqueness and stability of Lagrange multipliers for constrained optimization problems in abstract spaces. It is well known that validity of the strict…
Approximate directional stationarity and associated qualification conditions
Isabella Käming, Patrick Mehlitz
Approximate stationarity conditions provide necessary optimality conditions without requiring additional assumptions by demanding that a perturbed stationarity system possesses sol…
Augmented Lagrangian methods for fully convex composite optimization
Alberto De Marchi, Tim Hoheisel, Patrick Mehlitz
This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented…
Approximate stationarity in disjunctive optimization: concepts, qualification conditions, and application to MPCCs
Isabella Käming, Patrick Mehlitz
In this paper, we are concerned with stationarity conditions and qualification conditions for optimization problems with disjunctive constraints. This class covers, among others, o…
Revisiting implicit variables in mathematical optimization: simplified modeling and a numerical evidence
Patrick Mehlitz
Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence…
Duality-based single-level reformulations of bilevel optimization problems
Stephan Dempe, Patrick Mehlitz
Usually, bilevel optimization problems need to be transformed into single-level ones in order to derive optimality conditions and solution algorithms. Among the available approache…
On the directional asymptotic approach in optimization theory
Matúš Benko, Patrick Mehlitz
As a starting point of our research, we show that, for a fixed order , each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is eithe…
Isolated calmness of perturbation mappings in generalized nonlinear programming and local superlinear convergence of Newton-type methods
Matúš Benko, Patrick Mehlitz
In this paper, we characterize Lipschitzian properties of different multiplier-free and multiplier-dependent perturbation mappings associated with the stationarity system of a so-c…
Local properties and augmented Lagrangians in fully nonconvex composite optimization
Alberto De Marchi, Patrick Mehlitz
A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentia…
A fresh look at nonsmooth Levenberg--Marquardt methods with applications to bilevel optimization
Lateef O. Jolaoso, Patrick Mehlitz, Alain B. Zemkoho
In this paper, we revisit the classical problem of solving over-determined systems of nonsmooth equations numerically. We suggest a nonsmooth Levenberg--Marquardt method for its so…
Bilevel Optimal Control: Theory, Algorithms, and Applications
Stephan Dempe, Markus Friedemann, Felix Harder +2
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given meas…
Fuzzy multiplier, sum and intersection rules in non-Lipschitzian settings: decoupling approach revisited
Marián Fabian, Alexander Y. Kruger, Patrick Mehlitz
We revisit the decoupling approach widely used (often intuitively) in nonlinear analysis and optimization and initially formalized about a quarter of a century ago by Borwein & Zhu…
Variational Poisson Denoising via Augmented Lagrangian Methods
Christian Kanzow, Fabius Krämer, Patrick Mehlitz +2
In this paper, we denoise a given noisy image by minimizing a smoothness promoting function over a set of local similarity measures which compare the mean of the given image and so…
Notes on the value function approach to multiobjective bilevel optimization
Daniel Hoff, Patrick Mehlitz
This paper is concerned with the value function approach to multiobjective bilevel optimization which exploits a lower level frontier-type mapping in order to replace the hierarchi…
Convergence Analysis of the Proximal Gradient Method in the Presence of the Kurdyka-Łojasiewicz Property without Global Lipschitz Assumptions
Xiaoxi Jia, Christian Kanzow, Patrick Mehlitz
We consider a composite optimization problem where the sum of a continuously differentiable and a merely lower semicontinuous function has to be minimized. The proximal gradient al…
Inverse demand tracking in transportation networks
Simone Göttlich, Patrick Mehlitz, Thomas Schillinger
This paper deals with the reconstruction of the desired demand in an optimal control problem, stated over a tree-shaped transportation network which is governed by a linear hyperbo…
A simple proof of second-order sufficient optimality conditions in nonlinear semidefinite optimization
Patrick Mehlitz
In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization which does not rely on the enhance…
Why second-order sufficient conditions are, in a way, easy -- or -- revisiting calculus for second subderivatives
Matúš Benko, Patrick Mehlitz
In this paper, we readdress the classical topic of second-order sufficient optimality conditions for optimization problems with nonsmooth structure. Based on the so-called second s…
On the directional asymptotic approach in optimization theory Part B: constraint qualifications
Matúš Benko, Patrick Mehlitz
During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of…
On the directional asymptotic approach in optimization theory Part A: approximate, M-, and mixed-order stationarity
Matúš Benko, Patrick Mehlitz
We show that, for a fixed order , each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense…
Constrained composite optimization and augmented Lagrangian methods
Alberto De Marchi, Xiaoxi Jia, Christian Kanzow +1
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet s…