1 citations · 1 across the 14 of their papers we have counts for
18 papers
Galerkin approximations to the space of convex bodies by polytopes in nondegenerate V-representation
Janosch Rieger
We introduce finite-dimensional approximations to the space of convex bodies based on polytopes in vertex representation. For a prescribed set of directions, the admissible point c…
Restriction and interpolation operators for digital images and their boundaries
Janosch Rieger, Kyria Wawryk
The aim of this paper is to provide a coherent framework for transforming boundary pairs of digital images from one resolution to another without knowledge of the full images. It i…
Towards optimal space-time discretization for reachable sets of nonlinear control systems
Janosch Rieger, Kyria Wawryk
Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we exp…
Generalized Gearhart-Koshy acceleration for the Kaczmarz method
Janosch Rieger
The Kaczmarz method is an iterative numerical method for solving large and sparse rectangular systems of linear equations. Gearhart, Koshy and Tam have developed an acceleration te…
Backward-Forward-Reflected-Backward Splitting for Three Operator Monotone Inclusions
Janosch Rieger, Matthew K. Tam
In this work, we propose and analyse two splitting algorithms for finding a zero of the sum of three monotone operators, one of which is assumed to be Lipschitz continuous. Each it…
A learning-enhanced projection method for solving convex feasibility problems
Janosch Rieger
We propose a generalization of the method of cyclic projections, which uses the lengths of projection steps carried out in the past to learn about the geometry of the problem and d…
A linear programming approach to approximating the infinite time reachable set of strictly stable linear control systems
Andreas Ernst, Lars Grüne, Janosch Rieger
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that in…
Explicit Formula for Preimages of Relaxed One-Sided Lipschitz Mappings with Negative Lipschitz Constants
Andrew C. Eberhard, Boris S. Mordukhovich, Janosch Rieger
This paper addresses Lipschitzian stability issues that play an important role in both theoretical and numerical aspects of variational analysis, optimization, and their applicatio…
A Galerkin approach to optimization in the space of convex and compact subsets of
Janosch Rieger
The aim of this paper is to establish a theory of Galerkin approximations to the space of convex and compact subsets of with favorable properties, both from a theoretical an…
Semilinear Parabolic Differential Inclusions with One-sided Lipschitz Nonlinearities
Wolf-Jürgen Beyn, Etienne Emmrich, Janosch Rieger
We present an existence result for a partial differential inclusion with linear parabolic principal part and relaxed one-sided Lipschitz multivalued nonlinearity in the framework o…
Provably convergent implementations of the subdivision algorithm for the computation of invariant objects
Janosch Rieger
The subdivision algorithm by Dellnitz and Hohmann for the computation of invariant sets of dynamical systems decomposes the relevant region of the state space into boxes and analyz…
A reinterpretation of set differential equations as differential equations in a Banach space
Martin Rasmussen, Janosch Rieger, Kevin Webster
Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate se…
The Euler scheme for state constrained ordinary differential inclusions
Janosch Rieger
We propose and analyze a variation of the Euler scheme for state constrained ordinary differential inclusions under weak assumptions on the right-hand side and the state constraint…
On the solvability of relaxed one-sided Lipschitz inclusions in Hilbert spaces
Janosch Rieger, Tobias Weth
We prove solvability theorems for relaxed one-sided Lipschitz multivalued mappings in Hilbert spaces and for composed mappings in the Gelfand triple setting. From these theorems, w…
Approximation of reachable sets using optimal control and support vector machines
Martin Rasmussen, Janosch Rieger, Kevin Webster
We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorit…
Robust boundary tracking for reachable sets of nonlinear differential inclusions
Janosch Rieger
The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by thei…
Semi-implicit Euler schemes for ordinary differential inclusions
Janosch Rieger
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability…
A numerical method for the solution of relaxed one-sided Lipschitz algebraic inclusions
Wolf-Jürgen Beyn, Janosch Rieger
An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust n…