box-constraints

Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms

  • John W. Pearson
  • Margherita Porcelli
  • Martin Stoll
    • Categories Control Applications, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , , ,

    PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting L1 term within the objective function requires sophisticated optimization methods. We propose the use of an Interior Point scheme applied to a smoothed reformulation of the discretized problem, and … Read more

    An Infeasible Active Set Method with Combinatorial Line Search for Convex Quadratic Problems with Bound Constraints

  • Philipp Hungerländer
  • Franz Rendl
    • Categories Convex Optimization, Quadratic Programming Tags , , , ,

    The minimization of a convex quadratic function under bound constraints is a fundamental building block for more complicated optimization problems. The active-set method introduced by [M. Bergounioux, K. Ito, and K. Kunisch. Primal-Dual Strategy for Constrained Optimal Control Problems. SIAM Journal on Control and Optimization, 37:1176–1194, 1999.] and [M. Bergounioux, M. Haddou, M. Hintermüller, and … Read more

    A feasible active set method for strictly convex problems with simple bounds

  • Philipp Hungerländer
  • Franz Rendl
    • Categories Convex Optimization, Quadratic Programming Tags , , ,

    A primal-dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of [K. Kunisch and F. Rendl. An infeasible active set method for convex problems with simple bounds. SIAM Journal on Optimization, 14(1):35-52, 2003]. Based on a guess of the active set, a primal-dual pair (x,α) … Read more