Andreas Potschka

Reliable solution of convex quadratic programs with parametric active set methods

  • Hans Georg Bock
  • Christian Kirches
  • Andreas Potschka
  • Johannes P. Schlöder
    • Categories Convex Optimization, Optimization Software Benchmark, Quadratic Programming Tags , , ,

    Parametric Active Set Methods (PASM) are a relatively new class of methods to solve convex Quadratic Programming (QP) problems. They are based on tracing the solution along a linear homotopy between a QP with known solution and the QP to be solved. We explicitly identify numerical challenges in PASM and develop strategies to meet these … Read more

    Newton–Picard-Based Preconditioning for Linear-Quadratic Optimization Problems with Time-Periodic Parabolic PDE Constraints

  • Hans Georg Bock
  • Andreas Potschka
  • M.S. Mommer
  • Johannes P. Schlöder
    • Categories Optimization of Systems modeled by PDEs, Quadratic Programming Tags , , , ,

    We develop and investigate two preconditioners for a basic linear iterative splitting method for the numerical solution of linear-quadratic optimization problems with time-periodic parabolic PDE constraints. The resulting real-valued linear system to be solved is symmetric indefinite. We propose all-at-once symmetric indefinite preconditioners based on a Newton–Picard approach which divides the variable space into slow … Read more