time-domain decomposition

Time-Domain Decomposition for Mixed-Integer Optimal Control Problems

  • Falk M. Hante
  • Richard Krug
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , ,

    We consider mixed-integer optimal control problems, whose optimality conditions involve global combinatorial optimization aspects for the corresponding Hamiltonian pointwise in time. We propose a time-domain decomposition, which makes this problem class accessible for mixed-integer programming using parallel-in-time direct discretizations. The approach is based on a decomposition of the optimality system and the interpretation of the … 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