affine invariance

Affine invariant convergence rates of the conditional gradient method

  • Javier F. Peña
    • Categories Convex Optimization Tags , , ,

    We show that the conditional gradient method for the convex composite problem \[\min_x\{f(x) + \Psi(x)\}\] generates primal and dual iterates with a duality gap converging to zero provided a suitable growth property holds and the algorithm makes a judicious choice of stepsizes. The rate of convergence of the duality gap to zero ranges from sublinear … 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