56 citations · 162 across the 14 of their papers we have counts for
15 papers
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…
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…
The Sparse(st) Optimization Problem: Reformulations, Optimality, Stationarity, and Numerical Results
Christian Kanzow, Alexandra Schwarz, Felix Weiß
We consider the sparse optimization problem with nonlinear constraints and an objective function, which is given by the sum of a general smooth mapping and an additional term defin…
Efficient Regularized Proximal Quasi-Newton Methods for Large-Scale Nonconvex Composite Optimization Problems
Christian Kanzow, Theresa Lechner
Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited b…
Inexact Penalty Decomposition Methods for Optimization Problems with Geometric Constraints
Matteo Lapucci, Christian Kanzow
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular,…
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…
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…
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…
New Constraint Qualifications for Optimization Problems in Banach Spaces based on Asymptotic KKT Conditions
Eike Börgens, Christian Kanzow, Patrick Mehlitz +1
Optimization theory in Banach spaces suffers from the lack of available constraint qualifications. Despite the fact that there exist only a very few constraint qualifications, they…
Regularization of Limited Memory Quasi-Newton Methods for Large-Scale Nonconvex Minimization
Daniel Steck, Christian Kanzow
This paper deals with regularized Newton methods, a flexible class of unconstrained optimization algorithms that is competitive with line search and trust region methods and potent…
Quasi-Variational Inequalities in Banach Spaces: Theory and Augmented Lagrangian Methods
Christian Kanzow, Daniel Steck
This paper deals with quasi-variational inequality problems (QVIs) in a generic Banach space setting. We provide a theoretical framework for the analysis of such problems which is…
Relaxation schemes for mathematical programs with switching constraints
Christian Kanzow, Patrick Mehlitz, Daniel Steck
Switching-constrained optimization problems form a difficult class of mathematical programs since their feasible set is almost disconnected while standard constraint qualifications…
Augmented Lagrangian Methods for the Solution of Generalized Nash Equilibrium Problems
Christian Kanzow, Daniel Steck
We propose an augmented Lagrangian-type algorithm for the solution of generalized Nash equilibrium problems (GNEPs). Specifically, we discuss the convergence properties with regard…
An Augmented Lagrangian Method for Optimization Problems in Banach Spaces
Christian Kanzow, Daniel Steck, Daniel Wachsmuth
We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity o…
On Error Bounds and Multiplier Methods for Variational Problems in Banach Spaces
Christian Kanzow, Daniel Steck
This paper deals with a general form of variational problems in Banach spaces which encompasses variational inequalities as well as minimization problems. We prove a characterizati…