Günter Leugering

A Consensus-Based Alternating Direction Method for Mixed-Integer and PDE-Constrained Gas Transport Problems

  • Richard Krug
  • Günter Leugering
  • Alexander Martin
  • Martin Schmidt
  • Dieter Weninger
    • Categories (Mixed) Integer Nonlinear Programming, Network Optimization, Optimization of Systems modeled by PDEs Tags , , , ,

    We consider dynamic gas transport optimization problems, which lead to large-scale and nonconvex mixed-integer nonlinear optimization problems (MINLPs) on graphs. Usually, the resulting instances are too challenging to be solved by state-of-the-art MINLP solvers. In this paper, we use graph decompositions to obtain multiple optimization problems on smaller blocks, which can be solved in parallel … Read more

    Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems with Mixed Two-Point Boundary Conditions

  • Richard Krug
  • Günter Leugering
  • Martin Schmidt
  • Dieter Weninger
  • Alexander Martin
    • Categories Systems governed by Differential Equations Optimization Tags , , , ,

    In this article, we continue our work (Krug et al., 2021) on time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations in that we now consider mixed two-point boundary value problems and provide an in-depth well-posedness analysis. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems … Read more

    Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems

  • Richard Krug
  • Günter Leugering
  • Martin Schmidt
  • Dieter Weninger
  • Alexander Martin
    • Categories Systems governed by Differential Equations Optimization Tags , , , ,

    In this article, we extend the time-domain decomposition method described by Lagnese and Leugering (2003) to semilinear optimal control problems for hyperbolic balance laws with spatio-temporal varying coefficients. We provide the design of the iterative method applied to the global first-order optimality system, prove its convergence, and derive an a posteriori error estimate. The analysis … Read more

    Nonoverlapping Domain Decomposition for Optimal Control Problems governed by Semilinear Models for Gas Flow in Networks

  • Günter Leugering
  • Martin Schmidt
  • Mathias Sirvent
  • Alexander Martin
    • Categories Applications - Science and Engineering, Systems governed by Differential Equations Optimization Tags , , , ,

    We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a first-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order … Read more

    MIP-Based Instantaneous Control of Mixed-Integer PDE-Constrained Gas Transport Problems

  • Martin Gugat
  • Günter Leugering
  • Martin Schmidt
  • Mathias Sirvent
  • David Wintergerst
  • Alexander Martin
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , , ,

    We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations … Read more

    Towards Simulation Based Mixed-Integer Optimization with Differential Equations

  • Martin Gugat
  • Günter Leugering
  • Martin Schmidt
  • Mathias Sirvent
  • David Wintergerst
  • Alexander Martin
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Systems governed by Differential Equations Optimization Tags , , , ,

    We propose a decomposition based method for solving mixed-integer nonlinear optimization problems with “black-box” nonlinearities, where the latter, e.g., may arise due to differential equations or expensive simulation runs. The method alternatingly solves a mixed-integer linear master problem and a separation problem for iteratively refining the mixed-integer linear relaxation of the nonlinearity. We prove that … Read more

    Multidisciplinary Free Material Optimization

  • J Haslinger
  • Michal Kočvara
  • Günter Leugering
  • Michael Stingl
    • Categories Mechanical Engineering, Multidisciplinary Design Optimization, Semi-definite Programming Tags , , , ,

    We present a mathematical framework for the so-called multidisciplinary free material optimization (MDFMO) problems, a branch of structural optimization in which the full material tensor is considered as a design variable. We extend the original problem statement by a class of generic constraints depending either on the design or on the state variables. Among the … Read more

    Free Material Optimization with Fundamental Eigenfrequency Constraints.

  • Michal Kočvara
  • Günter Leugering
  • Michael Stingl
    • Categories Mechanical Engineering, Semi-definite Programming Tags , , ,

    The goal of this paper is to formulate and solve free material optimization problems with constraints on the smallest eigenfrequency of the optimal structure. A natural formulation of this problem as linear semidefinite program turns out to be numerically intractable. As an alternative, we propose a new approach, which is based on a nonlinear semidefinite … Read more

    Intensity based Three-Dimensional Reconstruction with Nonlinear Optimization

  • Martin Gugat
  • Günter Leugering
  • J. Hornegger
    • Categories Applications - Science and Engineering Tags , , ,

    New images of a three-dimensional scene can be generated from known image sequences using lightfields. To get high quality images, it is important to have accurate information about the structure of the scene. In order to optimize this information, we define a residual-function. This function represents the difference between an image, rendered in a known … Read more

    A Sequential Convex Semidefinite Programming Algorithm for Multiple-Load Free Material Optimization

  • Michal Kočvara
  • Günter Leugering
  • Michael Stingl
    • Categories Mechanical Engineering, Multidisciplinary Design Optimization, Semi-definite Programming Tags , ,

    A new method for the efficient solution of free material optimization problems is introduced. The method extends the sequential convex programming (SCP) concept to a class of optimization problems with matrix variables. The basic idea of the new method is to approximate the original optimization problem by a sequence of subproblems, in which nonlinear functions … Read more