10 papers
Projected Subgradient Methods for a Class of Nonsmooth and Nonconvex Optimization Problems
Christian Kanzow, Jannis Krüger, Leo Lehmann
We investigate the optimization problem of minimizing a nonsmooth function that satisfies a nonsmooth version of the descent lemma over a nonempty and closed but not necessarily co…
Convergence of the Safeguarded Augmented Lagrangian Method under the Polyak-Lojasiewicz constraint qualification for Constrained Composite Optimization
Christian Kanzow, Jannis Krüger
In this work we provide theoretical and practical results of the Safeguarded Augmented Lagrangian Method (SALM) for constrained composite optimization problems whose objective is t…
A Nonmonotone Descent Method for Optimization Problems Defined by Upper- Functions over Submanifolds
Christian Kanzow, Leo Lehmann
We consider the optimization problem of minimizing a nonsmooth function characterized by a nonsmooth formulation of the descent lemma over a manifold. In the unconstrained case ove…
Proximal Limited-Memory Quasi-Newton Methods for Nonsmooth Nonconvex Optimization
Simeon vom Dahl, Alberto De Marchi, Christian Kanzow
We propose a regularized proximal quasi-Newton method (RPQN) for minimizing the sum of a continuously differentiable, possibly nonconvex function and a proper, lower semicontinuous…
A modified exact penalty approach for general constrained -sparse optimization problems
Christian Kanzow, Felix Weiß
We consider a general class of constrained optimization problems with an additional - sparsity term in the objective function. Based on a recent reformulation of this diffi…
An adaptive proximal safeguarded augmented Lagrangian method for nonsmooth DC problems with convex constraints
Christian Kanzow, Tanja Neder
A proximal safeguarded augmented Lagrangian method for minimizing the difference of convex (DC) functions over a nonempty, closed and convex set with additional linear equality as…
Convergence of Nonmonotone Proximal Gradient Methods under the Kurdyka-Lojasiewicz Property without a Global Lipschitz Assumption
Christian Kanzow, Leo Lehmann
We consider the composite minimization problem with the objective function being the sum of a continuously differentiable and a merely lower semicontinuous and extended-valued func…
An Inexact Regularized Proximal Newton Method without Line Search
Simeon vom Dahl, Christian Kanzow
In this paper, we introduce an inexact regularized proximal Newton method (IRPNM) that does not require any line search. The method is designed to minimize the sum of a twice conti…
An Exact Penalty Approach for General -Sparse Optimization Problems
Christian Kanzow, Felix Weiß
We consider the general nonlinear optimization problem where the objective function has an additional term defined by the -quasi-norm in order to promote sparsity of a so…
Generalized Newton's Method based on Graphical Derivatives
T. Hoheisel, C. Kanzow, B. S. Mordukhovich +1
This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a n…