optimal control

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

    Different discretization techniques for solving optimal control problems with control complementarity constraints

  • Yu Deng
    • Categories Complementarity and Variational Inequalities, Infinite Dimensional Optimization Tags , , , ,

    There are first-optimize-then-discretize (indirect) and first-discretize-then-optimize (direct) methods to deal with infinite dimensional optimal problems numerically by use of finite element methods. Generally, both discretization techniques lead to different structures. Regarding the indirect method, one derives optimality conditions of the considered infinite dimensional problems in appropriate function spaces firstly and then discretizes them into suitable … Read more

    Central Limit Theorem and Sample Complexity of Stationary Stochastic Programs

  • Yi Cheng
  • Alexander Shapiro
    • Categories Stochastic Programming Tags , , , , , ,

    In this paper we discuss sample complexity of solving stationary stochastic programs by the Sample Average Approximation (SAA) method. We investigate this in the framework of Optimal Control (in discrete time) setting. In particular we derive a Central Limit Theorem type asymptotics for the optimal values of the SAA problems. The main conclusion is that … Read more

    Distributionally Robust Optimal Control and MDP Modeling

  • Alexander Shapiro
    • Categories Robust Optimization, Stochastic Programming Tags , , , , , , , ,

    In this paper, we discuss Optimal Control and Markov Decision Process (MDP) formulations of multistage optimization problems when the involved probability distributions are not known exactly, but rather are assumed to belong to specified ambiguity families. The aim of this paper is to clarify a connection between such distributionally robust approaches to multistage stochastic optimization. … Read more

    Solving Bang-Bang Problems Using The Immersed Interface Method and Integer Programming

  • Sarah Strikwerda
  • Ryan Vogt
    • Categories Combinatorial Optimization, Nonlinear Optimization Tags , , ,

    In this paper we study numerically solving optimal control problems with bang-bang control functions. We present a formal Lagrangian approach for solving the optimal control problem, and address difficulties encountered when numerically solving the state and adjoint equations by using the immersed interface method. We note that our numerical approach does not approximate the discontinuous … Read more

    Random-Sampling Monte-Carlo Tree Search Methods for Cost Approximation in Long-Horizon Optimal Control

  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering, Control Applications Tags , , ,

    We develop Monte-Carlo based heuristic approaches to approximate the objective function in long horizon optimal control problems. In these approaches, to approximate the expectation operator in the objective function, we evolve the system state over multiple trajectories into the future while sampling the noise disturbances at each time-step, and find the average (or weighted average) … 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

    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

    Global Dynamic Optimization with Hammerstein-Wiener Models Embedded

  • Dominik Bongartz
  • Alexander Mitsos
  • Jaromił Najman
  • C. D. Kappatou
  • S. Sass
    • Categories Global Optimization Theory Tags , , , ,

    Hammerstein-Wiener models constitute a significant class of block-structured dynamic models, as they approximate process nonlinearities on the basis of input-output data without requiring identification of a full nonlinear process model. Optimization problems with Hammerstein-Wiener models embedded are nonconvex, and thus local optimization methods may obtain suboptimal solutions. In this work, we develop a deterministic global … Read more

    KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

  • Drew P. Kouri
  • Denis Ridzal
  • Ray Tuminaro
    • Categories Control Applications, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the … Read more