Felix Lieder

Solving Large Scale Cubic Regularization by a Generalized Eigenvalue Problem

  • Felix Lieder
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems, Unconstrained Optimization Tags , ,

    Cubic Regularization methods have several favorable properties. In particular under mild assumptions, they are globally convergent towards critical points with second order necessary conditions satisfied. Their adoption among practitioners, however, does not yet match the strong theoretical results. One of the reasons for this discrepancy may be additional implementation complexity needed to solve the occurring … Read more

    On the Convergence Rate of the Halpern-Iteration

  • Felix Lieder
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , ,

    In this work, we give a tight estimate of the rate of convergence for the Halpern-Iteration for approximating a fixed point of a nonexpansive mapping in a Hilbert space. Specifically, we prove that the norm of the residuals is upper bounded by the distance of the initial iterate to the closest fixed point divided by … Read more

    On Affine Invariant Descent Directions

  • Yu-Hong Dai
  • Florian Jarre
  • Felix Lieder
    • Categories Nonlinear Optimization Tags , ,

    This paper explores the existence of affine invariant descent directions for unconstrained minimization. While there may exist several affine invariant descent directions for smooth functions $f$ at a given point, it is shown that for quadratic functions there exists exactly one invariant descent direction in the strictly convex case and generally none in the nondegenerate … Read more

    A Derivative-Free and Ready-to-Use NLP Solver for Matlab or Octave

  • Florian Jarre
  • Felix Lieder
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization Software and Modeling Systems Tags , ,

    This paper introduces a derivative-free and ready-to-use solver for nonlinear programs with nonlinear equality and inequality constraints (NLPs). Using finite differences and a sequential quadratic programming (SQP) approach, the algorithm aims at finding a local minimizer and no extra attempt is made to generate a globally optimal solution. Due to the use of finite differences, … Read more

    Simplified semidefinite and completely positive relaxations

  • Felix Lieder
    • Categories 0-1 Programming, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags ,

    This paper is concerned with completely positive and semidefinite relaxations of quadratic programs with linear constraints and binary variables as presented by Burer. It observes that all constraints of the relaxation associated with linear constraints of the original problem can be accumulated in a single linear constraint without changing the feasible set of either the … Read more

    Unifying semidefinite and set-copositive relaxations of binary problems and randomization techniques

  • Florian Jarre
  • Felix Lieder
  • Fatameh Bani Asadi Rad
    • Categories 0-1 Programming, Combinatorial Optimization Tags , , , , , ,

    A reformulation of quadratically constrained binary programs as duals of set-copositive linear optimization problems is derived using either \(\{0,1\}\)-formulations or \(\{-1,1\}\)-formulations. The latter representation allows an extension of the randomization technique by Goemans and Williamson. An application to the max-clique problem shows that the max-clique problem is equivalent to a linear program over the max-cut … Read more