55 citations · 86 across the 24 of their papers we have counts for
6 papers · 1 filter
Optimal Control of the Kirchhoff Equation
Masoumeh Hashemi, Roland Herzog, Thomas M. Surowiec
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed…
First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
Ronny Bergmann, Roland Herzog, Julián Ortiz López +1
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the cod…
An Optimal Control Problem for Single-Spot Pulsed Laser Welding
Roland Herzog, Dmytro Strelnikov
We consider an optimal control problem for a single-spot pulsed laser welding problem. The distribution of thermal energy is described by a quasilinear heat equation. Our emphasis…
A Discretize-Then-Optimize Approach to PDE-Constrained Shape Optimization
Roland Herzog, Estefanía Loayza-Romero
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admi…
Optimal Prediction using Learning and Shape Optimization
M. Sajjad Edalatzadeh, Roland Herzog
This paper investigates the problem of optimal predictor design for distributed parameter systems using neural networks and shape optimization. Sensors with various shapes are plac…
Fenchel Duality and a Separation Theorem on Hadamard Manifolds
Maurício Silva Louzeiro, Ronny Bergmann, Roland Herzog
In this paper, we introduce a definition of Fenchel conjugate and Fenchel biconjugate on Hadamard manifolds based on the tangent bundle. Our definition overcomes the inconvenience…