Andreas Potschka

A homotopy for the reliable estimation of model parameters in chromatography processes

  • Dominik H. Cebulla
  • Christian Kirches
  • Andreas Potschka
    • Categories Chemical Engineering, Nonlinear Systems and Least-Squares, Optimization of Systems modeled by PDEs Tags , , ,

    Mathematical modeling, simulation, and optimization can significantly support the development and characterization of chromatography steps in the biopharmaceutical industry. Particularly mechanistic models become preferably used, as these models, once carefully calibrated, can be employed for a reliable optimization. However, model calibration is a difficult task in this context due to high correlations between parameters, highly … Read more

    Mixed-Integer Optimal Control for Multimodal Chromatography

  • Hans Georg Bock
  • Christian Kirches
  • Andreas Potschka
  • Dominik H. Cebulla
    • Categories (Mixed) Integer Nonlinear Programming, Chemical Engineering, Systems governed by Differential Equations Optimization Tags , , ,

    Multimodal chromatography is a powerful tool in the downstream processing of biopharmaceuticals. To fully benefit from this technology, an efficient process strategy must be determined beforehand. To facilitate this task, we employ a recent mechanistic model for multimodal chromatography, which takes salt concentration and pH into account, and we present a mathematical framework for the … Read more

    Expert-Enhanced Machine Learning for Cardiac Arrhythmia Classification

  • Felix Bernhardt
  • Maximilian Merkert
  • Andreas Potschka
  • Sebastian Sager
  • Hugo Katus
  • Florian Kehrle
  • Benjamin Meder
  • Eberhard Scholz
    • Categories Biomedical Applications, Combinatorial Optimization Tags , , , , ,

    We propose a new method for the classification task of distinguishing atrial Fibrillation (AFib) from regular atrial tachycardias including atrial Flutter (AFlu) on the basis of a surface electrocardiogram (ECG). Although recently many approaches for an automatic classification of cardiac arrhythmia were proposed, to our knowledge none of them can distinguish between these two. We … Read more

    A partial outer convexification approach to control transmission lines

  • Simone Göttlich
  • Andreas Potschka
  • Claus Teuber
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs Tags , ,

    In this paper we derive an efficient optimization approach to calculate optimal controls of electric transmission lines. These controls consist of time-dependent inflows and switches that temporarily disable single arcs or whole subgrids to reallocate the flow inside the system. The aim is then to find the best energy input in terms of boundary controls … Read more

    Numerical solution of optimal control problems with explicit and implicit switches

  • Hans Georg Bock
  • Christian Kirches
  • Andreas Meyer
  • Andreas Potschka
    • Categories Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization

    In this article, we present a unified framework for the numerical solution of optimal control problems constrained by ordinary differential equations with both implicit and explicit switches. We present the problem class and qualify different types of implicitly switched systems. This classification significantly affects opportunities for solving such problems numerically. By using techniques from generalized … Read more

    trlib: A vector-free implementation of the GLTR method for iterative solution of the trust region problem

  • Christian Kirches
  • Andreas Potschka
  • Felix Lenders
    • Categories Optimization Software and Modeling Systems, Quadratic Programming Tags , , ,

    We describe trlib, a library that implements a Variant of Gould’s Generalized Lanczos method (Gould et al. in SIAM J. Opt. 9(2), 504–525, 1999) for solving the trust region problem. Our implementation has several distinct features that set it apart from preexisting ones. We implement both conjugate gradient (CG) and Lanczos iterations for assembly of … Read more

    Backward Step Control for Global Newton-type Methods

  • Andreas Potschka
    • Categories Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , ,

    We present and analyze a new damping approach called backward step control for the globalization of the convergence of Newton-type methods for the numerical solution of nonlinear root-finding problems. We provide and discuss reasonable assumptions that imply convergence of backward step control on the basis of generalized Newton paths in conjunction with a backward analysis … Read more

    Partial outer convexification for traffic light optimization in road networks

  • Simone Göttlich
  • Andreas Potschka
  • Ute Ziegler
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Transportation Tags , , , ,

    We consider the problem of computing optimal traffic light programs for urban road intersections using traffic flow conservation laws on networks. Based on a Partial Outer Convexification approach, which has been successfully applied in the area of mixed-integer optimal control for systems of ordinary or differential algebraic equations, we develop a computationally tractable two-stage solution … Read more

    A parametric active set method for quadratic programs with vanishing constraints

  • Hans Georg Bock
  • Christian Kirches
  • Andreas Potschka
  • Sebastian Sager
    • Categories Combinatorial Optimization, Control Applications, Quadratic Programming Tags , , ,

    Combinatorial and logic constraints arising in a number of challenging optimization applications can be formulated as vanishing constraints. Quadratic programs with vanishing constraints (QPVCs) then arise as subproblems during the numerical solution of such problems using algorithms of the Sequential Quadratic Programming type. QPVCs are nonconvex problems violating standard constraint qualifications. In this paper, we … Read more

    Reliable solution of convex quadratic programs with parametric active set methods

  • Hans Georg Bock
  • Christian Kirches
  • Andreas Potschka
  • Johannes P. Schlöder
    • Categories Convex Optimization, Optimization Software Benchmark, Quadratic Programming Tags , , ,

    Parametric Active Set Methods (PASM) are a relatively new class of methods to solve convex Quadratic Programming (QP) problems. They are based on tracing the solution along a linear homotopy between a QP with known solution and the QP to be solved. We explicitly identify numerical challenges in PASM and develop strategies to meet these … Read more