hybrid

An Accelerated Hybrid Proximal Extragradient Method for Convex Optimization and its Implications to Second-Order Methods

  • Renato D.C. Monteiro
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , , , , , ,

    This paper presents an accelerated variant of the hybrid proximal extragradient (HPE) method for convex optimization, referred to as the accelerated HPE (A-HPE) method. Iteration-complexity results are established for the A-HPE method, as well as a special version of it, where a large stepsize condition is imposed. Two specific implementations of the A-HPE method are … Read more

    Iteration-Complexity of a Newton Proximal Extragradient Method for Monotone Variational Inequalities and Inclusion Problems

  • Renato D.C. Monteiro
  • Benar Fux Svaiter
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization Tags , , , , , ,

    In a recent paper by Monteiro and Svaiter, a hybrid proximal extragradient framework has been used to study the iteration-complexity of a first-order (or, in the context of optimization, second-order) method for solving monotone nonlinear equations. The purpose of this paper is to extend this analysis to study a prox-type first-order method for monotone smooth … Read more