proximal point algorithm

Regularized HPE-type methods for solving monotone inclusions with improved pointwise iteration-complexity bounds

  • M. Marques Alves
  • Renato D.C. Monteiro
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the standard HPE method applied to regularizations of the original MIP. It is shown that its pointwise iteration-complexity considerably improves the one of the HPE method … Read more

    Inertial Proximal ADMM for Linearly Constrained Separable Convex Optimization

  • Raymond Chan
  • Caihua Chen
  • Shiqian Ma
  • Junfeng Yang
    • Categories Convex Optimization Tags , , , ,

    The \emph{alternating direction method of multipliers} (ADMM) is a popular and efficient first-order method that has recently found numerous applications, and the proximal ADMM is an important variant of it. The main contributions of this paper are the proposition and the analysis of a class of inertial proximal ADMMs, which unify the basic ideas of … Read more

    An Inexact Proximal Algorithm for Pseudomonotone and Quasimonotone Variational Inequalities

  • Lennin Mallma Ramirez
  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
    • Categories Nonsmooth Optimization Tags , , ,

    In this paper we introduce an inexact proximal point algorithm using proximal distances for solving variational inequality problems when the mapping is pseudomonotone or quasimonotone. Under some natural assumptions we prove that the sequence generates by the algorithm is convergent for the pseudomonotone case and weakly convergent for the quasimonotone ones. This approach unifies the … Read more

    On the convergence rate of an inexact proximal point algorithm for quasiconvex minimization on Hadamard manifolds

  • Nancy Baygorrea
  • Nelson Maculan
  • Erik Alex Papa Quiroz
    • Categories Global Optimization Tags , , , , ,

    In this paper we present a rate of convergence analysis of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem. Article Download View On the … Read more

    Inexact Proximal Point Methods for Quasiconvex Minimization on Hadamard Manifolds

  • Nancy Baygorrea
  • Nelson Maculan
  • Erik Alex Papa Quiroz
    • Categories Generalized Convexity/Monoticity, Global Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem. We also present an application of the method to demand theory … Read more

    Inertial primal-dual algorithms for structured convex optimization

  • Raymond Chan
  • Shiqian Ma
  • Junfeng Yang
    • Categories Convex and Nonsmooth Optimization Tags , , , , , ,

    The primal-dual algorithm recently proposed by Chambolle \& Pock (abbreviated as CPA) for structured convex optimization is very efficient and popular. It was shown by Chambolle \& Pock in \cite{CP11} and also by Shefi \& Teboulle in \cite{ST14} that CPA and variants are closely related to preconditioned versions of the popular alternating direction method of … Read more

    How the augmented Lagrangian algorithm can deal with an infeasible convex quadratic optimization problem

  • Alice Chiche
  • Jean Charles Gilbert
    • Categories Convex and Nonsmooth Optimization, Quadratic Programming Tags , , , , , , , , ,

    This paper analyses the behavior of the augmented Lagrangian algorithm when it deals with an infeasible convex quadratic optimization problem. It is shown that the algorithm finds a point that, on the one hand, satisfies the constraints shifted by the smallest possible shift that makes them feasible and, on the other hand, minimizes the objective … Read more

    Convergence rate analysis of primal-dual splitting schemes

  • Damek Davis
    • Categories Convex and Nonsmooth Optimization Tags , , , , , , , ,

    Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear compositions, and infimal convolutions of simple functions so that each simple term is processed individually via proximal mappings, gradient mappings, and … Read more

    Block-wise Alternating Direction Method of Multipliers for Multiple-block Convex Programming and Beyond

  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , , , , , ,

    The alternating direction method of multipliers (ADMM) is a benchmark for solving a linearly constrained convex minimization model with a two-block separable objective function; and it has been shown that its direct extension to a multiple-block case where the objective function is the sum of more than two functions is not necessarily convergent. For the … Read more

    A general inertial proximal point method for mixed variational inequality problem

  • Caihua Chen
  • Shiqian Ma
  • Junfeng Yang
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    In this paper, we first propose a general inertial proximal point method for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for inertial type proximal point methods. Under certain conditions, we are able to establish the global convergence and a $o(1/k)$ … Read more