second order necessary conditions

Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization

  • ClĂ©ment W. Royer
  • Stephen Wright
    • Categories Unconstrained Optimization Tags , , ,

    There has been much recent interest in finding unconstrained local minima of smooth functions, due in part of the prevalence of such problems in machine learning and robust statistics. A particular focus is algorithms with good complexity guarantees. Second-order Newton-type methods that make use of regularization and trust regions have been analyzed from such a … Read more

    A nonmonotone truncated Newton-Krylov method exploiting negative curvature directions, for large scale unconstrained optimization: complete results

  • Giovanni Fasano
  • Stefano Lucidi
    • Categories Unconstrained Optimization Tags , , , ,

    We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative … Read more