proximal algorithms

Double-Regularization Proximal Methods, with Complementarity Applications

  • Jonathan Eckstein
  • Paulo J. S. Silva
    • Categories Convex Optimization, Nonlinear Optimization Tags , ,

    We consider the variational inequality problem formed by a general set-valued maximal monotone operator and a possibly unbounded “box” in $R^n$, and study its solution by proximal methods whose distance regularizations are coercive over the box. We prove convergence for a class of double regularizations generalizing a previously-proposed class of Auslender et al. We apply … Read more

    A practical general approximation criterion for methods of multipliers based on Bregman distances

  • Jonathan Eckstein
    • Categories Convex Optimization Tags , , ,

    This paper demonstrates that for generalized methods of multipliers for convex programming based on Bregman distance kernels — including the classical quadratic method of multipliers — the minimization of the augmented Lagrangian can be truncated using a simple, generally implementable stopping criterion based only on the norms of the primal iterate and the gradient (or … Read more