augmented Lagrangian

Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

  • Robert Baraldi
  • Stefan M. Wild
  • Sven Leyffer
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , ,

    Nonconvex, nonlinear cost functions arise naturally in physical inverse problems and machine learning. The alternating direction method of multipliers (ADMM) has seen extensive use in these applications, despite exhibiting uncertain convergence behavior in many practical nonconvex settings, and struggling with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential … Read more

    A low-rank augmented Lagrangian method for large-scale semidefinite programming based on a hybrid convex-nonconvex approach

  • Renato D.C. Monteiro
  • Arnesh Sujanani
  • Diego Cifuentes
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , , , ,

    \(\) This paper introduces HALLaR, a new first-order method for solving large-scale semidefinite programs (SDPs) with bounded domain. HALLaR is an inexact augmented Lagrangian (AL) method where the AL subproblems are solved by a novel hybrid low-rank (HLR) method. The recipe behind HLR is based on two key ingredients: 1) an adaptive inexact proximal point … Read more

    On the paper “Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem”

  • Luís Felipe Bueno
  • Gabriel Haeser
  • Oliver Kolossoski
    • Categories Nonlinear Optimization Tags , ,

    In the paper [Torrealba, E.M.R. et al. Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem. EJOR, 299(1) 46–59, 2021] an augmented Lagrangian algorithm was proposed for resource allocation problems with the intriguing characteristic that instead of solving the box-constrained augmented Lagrangian subproblem, they propose projecting the solution of the unconstrained subproblem onto … Read more

    Inexact Penalty Decomposition Methods for Optimization Problems with Geometric Constraints

  • Christian Kanzow
  • Matteo Lapucci
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , , ,

    This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some  situations where parts of the constraints are nonconvex and complicated, like cardinality constraints, disjunctive programs, or matrix problems involving rank constraints. By a variable duplication and  decomposition strategy, … Read more

    A primal-dual majorization-minimization method for large-scale linear programs

  • Xin-Wei Liu
  • Yu-Hong Dai
  • Yakui Huang
    • Categories Linear Programming Tags , , , ,

    We present a primal-dual majorization-minimization method for solving large-scale linear programs. A smooth barrier augmented Lagrangian (SBAL) function with strict convexity for the dual linear program is derived. The majorization-minimization approach is naturally introduced to develop the smoothness and convexity of the SBAL function. Our method only depends on a factorization of the constant matrix … Read more

    A Globally Convergent Distributed Jacobi Scheme for Block-Structured Nonconvex Constrained Optimization Problems

  • Anirudh Subramanyam
  • Youngdae Kim
  • Michel Schanen
  • François Pacaud
  • Mihai Anitescu
    • Categories Constrained Nonlinear Optimization Tags , ,

    Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs Jacobi-type proximal updates of the augmented Lagrangian function, requiring only local solutions of separable block nonlinear programming (NLP) problems. We provide a cheap and explicitly computable Lyapunov function that allows … Read more