second-order

Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

  • Nadav Hallak
  • Marc Teboulle
    • Categories Constrained Nonlinear Optimization Tags , ,

    This paper introduces a method for computing points satisfying the second-order necessary optimality conditions in constrained nonconvex minimization. The method comprises two independent steps corresponding to the first and second order conditions. The first-order step is a generic closed map algorithm which can be chosen from a variety of first-order algorithms, making it The second-order … Read more

    A second-order globally convergent direct-search method and its worst-case complexity

  • Serge Gratton
  • ClĂ©ment W. Royer
  • Luis Nunes Vicente
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    Direct-search algorithms form one of the main classes of algorithms for smooth unconstrained derivative-free optimization, due to their simplicity and their well-established convergence results. They proceed by iteratively looking for improvement along some vectors or directions. In the presence of smoothness, first-order global convergence comes from the ability of the vectors to approximate the steepest … Read more

    Partial Smoothness,Tilt Stability, and Generalized Hessians

  • Adrian Lewis
  • Shanshan Zhang
    • Categories Nonsmooth Optimization Tags , , , , , , , ,

    We compare two recent variational-analytic approaches to second-order conditions and sensitivity analysis for nonsmooth optimization. We describe a broad setting where computing the generalized Hessian of Mordukhovich is easy. In this setting, the idea of tilt stability introduced by Poliquin and Rockafellar is equivalent to a classical smooth second-order condition. ArticleDownload View PDF