Randomized Roundings for a Mixed-Integer Elliptic Control System

  • Martin T. Köhler
  • Lauri Kröger
  • Christian Kirches
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , Short URL: https://optimization-online.org/?p=27629

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    We present randomized reconstruction approaches for optimal solutions to mixed-integer elliptic PDE control systems. Approximation properties and relations to sum-up rounding are derived using the cut norm. This enables us to dispose of space-filling curves required for sum-up rounding. Rates of almost sure convergence in the cut norm and the SUR norm in control space as well as almost sure \(H^1\) convergence in state space are shown.

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