Systems governed by Differential Equations Optimization

NONSMOOTH OPTIMIZATION OVER THE (WEAKLY OR PROPERLY) PARETO SET OF A LINEAR-QUADRATIC MULTI-OBJECTIVE CONTROL PROBLEM : EXPLICIT OPTIMALITY CONDITIONS

  • Henri Bonnel
  • Ngoc Sang Pham
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization, Systems governed by Differential Equations Optimization Tags , ,

    We present explicit optimality conditions for a nonsmooth functional defined over the (properly or weakly) Pareto set associated to a multiobjective linear-quadratic control problem. This problem is very difficult even in a finite dimensional setting, i.e. when, instead of a control problem, we deal with a mathematical programming problem. Amongst different applications, our problem may … Read more

    Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions

  • Samir Adly
  • Abderrahim Hantoute
  • Michel Thera
    • Categories Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , , , ,

    The main objective of this paper is to provide new explicit criteria to characterize weak lower semi-continuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by the means of the proximal … Read more

    Convergence and Descent Properties for a Class of Multilevel Optimization Algorithms

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

    I present a multilevel optimization approach (termed MG/Opt) for the solution of constrained optimization problems. The approach assumes that one has a hierarchy of models, ordered from fine to coarse, of an underlying optimization problem, and that one is interested in finding solutions at the finest level of detail. In this hierarchy of models calculations … Read more

    Lipschitz solutions of optimal control problems with state constraints of arbitrary order

  • Joseph Frédéric Bonnans
    • Categories Control Applications, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , ,

    In this paper we generalize to an arbitrary order, under minimal hypotheses, some sufficient conditions for Lipschitz continuity of the solution of a state constrained optimal control problems. The proof combines the approach by Hager in 1979 for dealing with first-order state constraints, and the high-order alternative formulation of the optimality conditions. CitationPublished as INRIA … Read more

    A Collection of 1,300 Dynamical Systems for Testing Data Fitting, Optimal Control, Experimental Design, Identification, Simulation or Similar Software – User’s Guide

  • Klaus Schittkowski
    • Categories Modeling Languages and Systems, Optimization Software Benchmark, Systems governed by Differential Equations Optimization

    We describe a collection of test problems which have been used to develop and test data fitting software for identifying parameters in explicit model functions, dynamical systems of equations, Laplace transformations, systems of ordinary differential equations, differential algebraic equations, or systems of one-dimensional time-dependent partial differential equations with or without algebraic equations. The test cases … Read more

    Data Fitting and Experimental Design in Dynamical Systems with EASY-FIT ModelDesign

  • Klaus Schittkowski
    • Categories Nonlinear Systems and Least-Squares, Problem Solving Environments, Systems governed by Differential Equations Optimization

    EASY-FIT is an interactive software system to identify parameters and compute optimal designs in explicit model functions, steady-state systems, Laplace transformations, systems of ordinary differential equations, differential algebraic equations, or systems of one-dimensional time dependent partial differential equations with or without algebraic equations. Proceeding from given experimental data, i.e. observation times and measurements, the minimum … Read more

    A Factorization with Update Procedures for a KKT Matrix Arising in Direct Optimal Control

  • Hans Georg Bock
  • Christian Kirches
  • Sebastian Sager
  • Johannes P. Schlöder
    • Categories Quadratic Programming, Systems governed by Differential Equations Optimization Tags , ,

    Quadratic programs obtained for optimal control problems of dynamic or discrete–time processes usually involve highly block structured Hessian and constraints matrices. Efficient numerical methods for the solution of such QPs have to respect and exploit this block structure. In interior point methods, this is elegantly achieved by the widespread availability of advanced sparse symmetric indefinite … Read more

    Block Structured Quadratic Programming for the Direct Multiple Shooting Method for Optimal Control

  • Hans Georg Bock
  • Christian Kirches
  • Sebastian Sager
  • Johannes P. Schlöder
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming, Systems governed by Differential Equations Optimization Tags , ,

    In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems arise, e.g., from the outer convexification of integer control decisions. We treat this optimal control problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved … Read more

    The Integer Approximation Error in Mixed-Integer Optimal Control

  • Hans Georg Bock
  • Moritz Diehl
  • Sebastian Sager
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , ,

    We extend recent work on nonlinear optimal control problems with integer restrictions on some of the control functions (mixed-integer optimal control problems, MIOCP) in two ways. We improve a theorem that states that the solution of a relaxed and convexified problem can be approximated with arbitrary precision by a solution fulfilling the integer requirements. Unlike … Read more

    A Fast Moving Horizon Estimation Algorithm Based on Nonlinear Programming Sensitivity

  • Lorenz T. Biegler
  • Carl D. Laird
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    Moving Horizon Estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has been mainly due to the difficulty to solve, in real-time, the associated dynamic optimization problems. In this work, a fast MHE algorithm able to overcome this … Read more