majorization-minimization method

First-order Methods for Unconstrained Vector Optimization Problems: A Unified Majorization-Minimization Perspective

  • Jian Chen
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    In this paper, we develop a unified majorization-minimization scheme and convergence analysis with first-order surrogate functions for unconstrained vector optimization problems (VOPs). By selecting different surrogate functions, the unified method can be reduced to various existing first-order methods. The unified convergence analysis reveals that the slow convergence of the steepest descent method is primarily attributed … Read more

    A Majorization-Minimization approach for multiclass classification in a big data scenario

  • Giorgia Franchini
  • Federica Porta
  • Émilie Chouzenoux
  • Jean-Christophe Pesquet
  • filippo.camellini
    • Categories Convex Optimization, Data Science Algorithms, Unconstrained Optimization Tags , , , , ,

    This work presents a novel optimization approach for training linear classifiers in multiclass classification tasks, when focusing on a regularized and smooth Weston-Watkins support vector machine (SVM) model. We propose a Majorization-Minimization (MM) algorithm to solve the resulting, Lipschitz-differentiable, optimization problem. To enhance scalability of the algorithm when tackling large datasets, we introduce an incremental … 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