Unconstrained Optimization

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