Christian Kirches

Switching cost aware rounding for relaxations of mixed-integer optimal control problems: the two-dimensional case

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications Tags ,

    This article is concerned with a recently proposed switching cost aware rounding (SCARP) strategy in the combinatorial integral decomposition for mixed-integer optimal control problems (MIOCPs). We consider the case of a control variable that is discrete-valued and distributed on a two-dimensional domain. While the theoretical results from the one-dimensional case directly apply to the multidimensional … Read more

    Matching Algorithms and Complexity Results for Constrained Mixed-Integer Optimal Control with Switching Costs

  • Felix Bestehorn
  • Christian Kirches
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms Tags , , , ,

    We extend recent work on the performance of the combinatorial integral approximation decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs) in the presence of combinatorial constraints or switching costs on an equidistant grid. For the time discretized problem, we reformulate the emerging rounding problem in the decomposition approach as a matching problem on a bipartite … 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

    Mixed-Integer Optimal Control Problems with switching costs: A shortest path approach

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms Tags , , , ,

    We investigate an extension of Mixed-Integer Optimal Control Problems (MIOCPs) by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the … Read more

    Relations Between Abs-Normal NLPs and MPCCs Part 2: Weak Constraint Qualifications

  • Lisa Hegerhorst-Schultchen
  • Christian Kirches
  • Marc C. Steinbach
    • Categories Nonsmooth Optimization Tags , , , ,

    This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie’s and Guignard’s kink qualification and … Read more

    Relations Between Abs-Normal NLPs and MPCCs Part 1: Strong Constraint Qualifications

  • Lisa Hegerhorst-Schultchen
  • Christian Kirches
  • Marc C. Steinbach
    • Categories Nonsmooth Optimization Tags , , , ,

    This work is part of an ongoing effort of comparing non-smooth optimization problems in abs-normal form to MPCCs. We study the general abs-normal NLP with equality and inequality constraints in relation to an equivalent MPCC reformulation. We show that kink qualifications and MPCC constraint qualifications of linear independence type and Mangasarian-Fromovitz type are equivalent. Then … Read more

    Efficient Derivative Evaluation for Rigid-body Dynamics based on Recursive Algorithms subject to Kinematic and Loop Constraints

  • Christian Kirches
  • Manuel Kudruss
  • Paul Manns
    • Categories Control Applications

    Simulation, optimization and control of robotic and bio-mechanical systems depend on a mathematical model description, typically a rigid-body system connected by joints, for which efficient algorithms to compute the forward or inverse dynamics exist. Models that e.g.\ include spring-damper systems are subject to both kinematic and loop constraints. Gradient-based optimization and control methods require derivatives … Read more

    A switching cost aware rounding method for relaxations of mixed-integer optimal control problems

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags ,

    This article investigates a class of Mixed-Integer Optimal Control Problems (MIOCPs) with switching costs. We introduce the problem class of Minimal-Switching-Cost Optimal Control Problems (MSCP) with an objective function that consists of two summands, a continuous term depending on the state vector and an encoding of the discrete switching costs. State vectors of Mixed-Integer Optimal … Read more

    Numerical Solution of Optimal Control Problems with Switches, Switching Costs and Jumps

  • Christian Kirches
  • Ekaterina Kostina
  • Andreas Meyer
  • Matthias Schlöder
    • Categories Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization

    In this article, we present a framework for the numerical solution of optimal control problems, constrained by ordinary differential equations which can run in (finitely many) different modes, where a change of modes leads to additional switching cost in the cost function, and whenever the system changes its mode, jumps in the differential states are … Read more

    On the Relation between MPECs and Optimization Problems in Abs-Normal Form

  • Lisa Hegerhorst-Schultchen
  • Christian Kirches
  • Marc C. Steinbach
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    We show that the problem of unconstrained minimization of a function in abs-normal form is equivalent to identifying a certain stationary point of a counterpart Mathematical Program with Equilibrium Constraints (MPEC). Hence, concepts introduced for the abs-normal forms turn out to be closely related to established concepts in the theory of MPECs. We give a … Read more