Systems governed by Differential Equations Optimization

Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control

  • Benoit Chachuat
  • Boris Houska
    • Categories Global Optimization Theory, Systems governed by Differential Equations Optimization

    This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a spatial branch-and-bound algorithm. A new operation, called lifting, is introduced which refines the control parameterization via a Gram-Schmidt orthogonalization … Read more

    Sensitivity analysis for relaxed optimal control problems with final-state constraints

  • Joseph Frédéric Bonnans
  • Laurent Pfeiffer
  • Oana Silvia Serea
    • Categories Systems governed by Differential Equations Optimization Tags , , , , ,

    In this article, we compute a second-order expansion of the value function of a family of relaxed optimal control problems with final-state constraints, parameterized by a perturbation variable. The sensitivity analysis is performed for controls that we call R-strong solutions. They are optimal solutions with respect to the set of feasible controls with a uniform … Read more

    Using Inexact Gradients in a Multilevel Optimization Algorithm

  • Michael Lewis
  • Stephen G. Nash
    • Categories Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    Many optimization algorithms require gradients of the model functions, but computing accurate gradients can be computationally expensive. We study the implications of using inexact gradients in the context of the multilevel optimization algorithm MGOpt. MGOpt recursively uses (typically cheaper) coarse models to obtain search directions for finer-level models. However, MGOpt requires the gradient on the … Read more

    Squeeze-and-Breathe Evolutionary Monte Carlo Optimisation with Local Search Acceleration and its application to parameter fitting

  • Mauricio Barahona
  • Mariano Beguerisse-Díaz
  • Radhika Desikan
  • Baojun Wang
    • Categories Applications - Science and Engineering, Global Optimization Applications, Systems governed by Differential Equations Optimization Tags , , , ,

    Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy data sets. Over the years, a variety of heuristics have been proposed to solve this complex optimisation problem, with good results in some cases yet with limitations in … Read more

    Parallel algebraic multilevel Schwarz preconditioners for a class of elliptic PDE systems

  • Alfio Borzì
  • Valentina De Simone
  • Daniela di Serafino
    • Categories Systems governed by Differential Equations Optimization Tags , , , ,

    We present algebraic multilevel preconditioners for linear systems arising from the discretization of systems of coupled elliptic partial differential equations (PDEs). These preconditioners are based on modifications of Schwarz methods and of the smoothed aggregation technique, where the coarsening strategy and the restriction and prolongation operators are defined using a point-based approach with a primary … Read more

    On the Difficulty of Deciding Asymptotic Stability of Cubic Homogeneous Vector Fields

  • Amir Ali Ahmadi
    • Categories Control Applications, Semi-definite Programming, Systems governed by Differential Equations Optimization Tags , ,

    It is well-known that asymptotic stability (AS) of homogeneous polynomial vector fields of degree one (i.e., linear systems) can be decided in polynomial time e.g. by searching for a quadratic Lyapunov function. Since homogeneous vector fields of even degree can never be AS, the next interesting degree to consider is equal to three. In this … Read more

    TACO – A Toolkit for AMPL Control Optimization

  • Christian Kirches
  • Sven Leyffer
    • Categories Modeling Languages and Systems, Problem Solving Environments, Systems governed by Differential Equations Optimization

    We describe a set of extensions to the AMPL modeling language to conveniently model mixed-integer optimal control problems for ODE or DAE dynamic processes. These extensions are realized as AMPL user functions and suffixes and do not require intrusive changes to the AMPL language standard or implementation itself. We describe and provide TACO, a Toolkit … Read more

    Efficient Direct Multiple Shooting for Nonlinear Model Predictive Control on Long Horizons

  • Hans Georg Bock
  • Christian Kirches
  • Johannes P. Schlöder
  • Leonard Wirsching
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    We address direct multiple shooting based algorithms for nonlinear model predictive control, with a focus on problems with long prediction horizons. We describe different efficient multiple shooting variants with a computational effort that is only linear in the horizon length. Proposed techniques comprise structure exploiting linear algebra on the one hand, and approximation of derivative … Read more

    Sampling Decisions in Optimum Experimental Design in the Light of Pontryagin’s Maximum Principle

  • Sebastian Sager
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , ,

    Optimum Experimental Design (OED) problems are optimization problems in which an experimental setting and decisions on when to measure – the so-called sampling design – are to be determined such that a follow-up parameter estimation yields accurate results for model parameters. In this paper we use the interpretation of OED as optimal control problems with … Read more

    A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions

  • Hédy Attouch
  • Benar Fux Svaiter
    • Categories Complementarity and Variational Inequalities, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , , , , , ,

    We introduce non-autonomous continuous dynamical systems which are linked to Newton and Levenberg-Marquardt methods. They aim at solving inclusions governed by maximal monotone operators in Hilbert spaces. Relying on Minty representation of maximal monotone operators as lipschitzian manifolds, we show that these dynamics can be formulated as first-order in time differential systems, which are relevant … Read more