Composite Minimization

Accelerated proximal gradient algorithm for weakly convex function

  • Milan Barik
  • Suvendu Ranjan Pattanaik
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

    In this work, we investigate the accelerated proximal gradient algorithm (APGα) for weakly convex composite optimization problems. Building upon the framework of B¨ohm and Wright, and additionally assuming that f is convex and coercive while g is bounded below, we establish an objective residual convergence rate of O(1⁄j²) for α≥3. Moreover, when α›3, this rate … Read more

    Adaptive Third-Order Methods for Composite Convex Optimization

  • Geovani Nunes Grapiglia
  • Yurii Nesterov
    • Categories Convex Optimization Tags , ,

    In this paper we propose third-order methods for composite convex optimization problems in which the smooth part is a three-times continuously differentiable function with Lipschitz continuous third-order derivatives. The methods are adaptive in the sense that they do not require the knowledge of the Lipschitz constant. Trial points are computed by the inexact minimization of … Read more