John W. Pearson

A New Preconditioning Approach for an Interior Point-Proximal Method of Multipliers for Linear and Convex Quadratic Programming

  • Luca Bergamaschi
  • Jacek Gondzio
  • John W. Pearson
  • Ángeles Martínez
  • Spyridon Pougkakiotis
    • Categories Convex Optimization, Linear Programming, Quadratic Programming Tags , , , ,

    In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers, which in turn results in a primal-dual regularized interior point method. Application of this method gives rise to a … Read more

    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