relaxations of mixed integer optimal control

Improved Regularity Assumptions for Partial Outer Convexification of Mixed-Integer PDE-Constrained Optimization problems

  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , ,

    Partial outer convexification is a relaxation technique for MIOCPs being constrained by time-dependent differential equations. Sum-Up-Rounding algorithms allow to approximate feasible points of the relaxed, convexified continuous problem with binary ones that are feasible up to an arbitrarily small $\delta > 0$. We show that this approximation property holds for ODEs and semilinear PDEs under … Read more

    Approximation Properties of Sum-Up Rounding in the Presence of Vanishing Constraints

  • Christian Kirches
  • Felix Lenders
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms, Systems governed by Differential Equations Optimization Tags , ,

    Approximation algorithms like sum-up rounding that allow to compute integer-valued approximations of the continuous controls in a weak$^*$ sense have attracted interest recently. They allow to approximate (optimal) feasible solutions of continuous relaxations of mixed-integer control problems (MIOCPs) with integer controls arbitrarily close. To this end, they use compactness properties of the underlying state equation, … Read more