Unconstrained Optimization

A Computational Study of a Gradient-Based Log-Barrier Algorithm for a Class of Large-Scale SDPs

  • Samuel Burer
  • Renato D.C. Monteiro
  • Yin Zhang
    • Categories Combinatorial Optimization, Semi-definite Programming, Unconstrained Optimization Tags , , , ,

    The authors of this paper recently introduced a transformation \cite{BuMoZh99-1} that converts a class of semidefinite programs (SDPs) into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation enables the application of nonlinear optimization techniques to the solution of certain SDPs that are too large for conventional interior-point methods to handle efficiently. Based … Read more

    On the Convergence of Newton Iterations to Non-Stationary Points

  • Richard H. Byrd
  • Marcelo Marazzi
  • Jorge Nocedal
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , ,

    We study conditions under which line search Newton methods for nonlinear systems of equations and optimization fail due to the presence of singular non-stationary points. These points are not solutions of the problem and are characterized by the fact that Jacobian or Hessian matrices are singular. It is shown that, for systems of nonlinear equations, … Read more

    Extra-Updates Criterion for the Limited Memory BFGS Algorithm for Large Scale Nonlinear Optimization

  • Mehiddin Al-Baali
    • Categories Unconstrained Optimization Tags , ,

    This paper studies recent modifications of the limited memory BFGS (L-BFGS) method for solving large scale unconstrained optimization problems. Each modification technique attempts to improve the quality of the L-BFGS Hessian by employing (extra) updates in certain sense. Because at some iterations these updates might be redundant or worsen the quality of this Hessian, this … Read more

    Convergence Results for Pattern Search Algorithms are Tight

  • Charles Audet
    • Categories Unconstrained Optimization Tags , , ,

    Recently, general definitions of pattern search methods for both unconstrained and linearly constrained optimization were presented. It was shown under mild conditions, that there exists a subsequence of iterates converging to a stationary point. In the unconstrained case, stronger results are derived under additional assumptions. In this paper, we present three small dimensioned examples showing … Read more