regularized newton methods

Solving a linear program via a single unconstrained minimization

  • Adilet Otemissov
  • Alina Abdikarimova
    • Categories Linear Programming, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , , , ,

    This paper proposes a novel approach for solving linear programs. We reformulate a primal-dual linear program as an unconstrained minimization of a convex and twice continuously differentiable merit function. When the optimal set of the primal-dual pair is nonempty, its optimal set is equal to the optimal set of the proposed merit function. Minimizing this … Read more

    A regularized limited-memory BFGS method for unconstrained minimization problems

  • Shinji Sugimoto
  • Nobuo Yamashita
    • Categories Unconstrained Optimization Tags , ,

    The limited-memory BFGS (L-BFGS) algorithm is a popular method of solving large-scale unconstrained minimization problems. Since L-BFGS conducts a line search with the Wolfe condition, it may require many function evaluations for ill-posed problems. To overcome this difficulty, we propose a method that combines L-BFGS with the regularized Newton method. The computational cost for a … Read more