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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…
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…
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…
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…
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…