Optimization of Systems modeled by PDEs

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

    Automatic Differentiation of the Open CASCADE Technology CAD System and its coupling with an Adjoint CFD Solver

  • Salvatore Auriemma
  • Herve Legrand
  • Mladen Banovic
  • Jens-Dominik Müller
  • Orest Mykhaskiv
  • Andrea Walther
    • Categories Optimization of Systems modeled by PDEs, Unconstrained Optimization Tags , , ,

    Automatic Differentiation (AD) is applied to the open-source CAD system Open CASCADE Technology using the AD software tool ADOL-C (Automatic Differentiation by OverLoading in C++). The differentiated CAD system is coupled with a discrete adjoint CFD solver, thus providing the first example of a complete differentiated design chain built from generic, multi-purpose tools. The design … Read more

    pyomo.dae: A Modeling and Automatic Discretization Framework for Optimization with Differential and Algebraic Equations

  • Lorenz T. Biegler
  • Jean-Paul Watson
  • Victor M. Zavala
  • Bethany Nicholson
  • John D. Siirola
    • Categories Modeling Languages and Systems, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , , ,

    We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http: //www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, … Read more

    Constrained Optimization with Low-Rank Tensors and Applications to Parametric Problems with PDEs

  • Sebastian Garreis
  • Michael Ulbrich
    • Categories Optimization of Systems modeled by PDEs, Stochastic Programming, Systems governed by Differential Equations Optimization Tags , , , , , , ,

    Low-rank tensor methods provide efficient representations and computations for high-dimensional problems and are able to break the curse of dimensionality when dealing with systems involving multiple parameters. We present algorithms for constrained nonlinear optimization problems that use low-rank tensors and apply them to optimal control of PDEs with uncertain parameters and to parametrized variational inequalities. … 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 basis-free null space method for solving generalized saddle point problems

  • Maria A. Diniz-Ehrhardt
  • Lucas G. Pedroso
  • Douglas Mendes
    • Categories Constrained Nonlinear Optimization, Optimization of Systems modeled by PDEs Tags , , , , , , ,

    Using an augmented Lagrangian matrix approach, we analytically solve in this paper a broad class of linear systems that includes symmetric and nonsymmetric problems in saddle point form. To this end, some mild assumptions are made and a preconditioning is specially designed to improve the sensitivity of the systems before the calculation of their solutions. … Read more

    On Theoretical and Numerical Aspects of the Shape Sensitivity Analysis for the 3D Time-dependent Maxwell’s Equations

  • Stephan Schmidt
  • Maria Schütte
  • Andrea Walther
    • Categories Optimization of Systems modeled by PDEs Tags , , , , ,

    We propose a novel approach using shape derivatives to solve inverse optimization problems governed by Maxwell’s equations, focusing on identifying hidden geometric objects in a predefined domain. The target functional is of tracking type and determines the distance between the solution of a 3D time-dependent Maxwell problem and given measured data in an $L_2$-norm. Minimization … Read more

    Thermal Optimization of the Continuous Casting Process using Distributed Parameter Identification Approach — Controlling the Curvature of Solid-Liquid Interface

  • Rouhollah Tavakoli
    • Categories Applications - Science and Engineering, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs

    Thermal optimization of vertical continuous casting process is considered in the present study. The goal is to find the optimal distribution of temperature and interfacial heat transfer coefficients corresponding to the primary and secondary cooling systems, in addition to the pulling speed, such that the solidification along the main axis of strand approaches to the … Read more

    Unconditionally energy stable time stepping scheme for Cahn-Morral equation: application to multi-component spinodal decomposition and optimal space tiling

  • Rouhollah Tavakoli
    • Categories Applications - Science and Engineering, Basic Sciences Applications, Optimization of Systems modeled by PDEs Tags , , , , , ,

    An unconditionally energy stable time stepping scheme is introduced to solve Cahn-Morral-like equations in the present study. It is constructed based on the combination of David Eyre’s time stepping scheme and Schur complement approach. Although the presented method is general and independent to the choice of homogeneous free energy density function term, logarithmic and polynomial … Read more

    A Flexible Iterative Solver for Nonconvex, Equality-Constrained Quadratic Subproblems

  • Alp Dener
  • Jason Hicken
    • Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , , , , ,

    We present an iterative primal-dual solver for nonconvex equality-constrained quadratic optimization subproblems. The solver constructs the primal and dual trial steps from the subspace generated by the generalized Arnoldi procedure used in flexible GMRES (FGMRES). This permits the use of a wide range of preconditioners for the primal-dual system. In contrast with FGMRES, the proposed … Read more