quadratic interpolation

Modeling Hessian-vector products in nonlinear optimization: New Hessian-free methods

  • L. Song
  • Luis Nunes Vicente
    • Categories Unconstrained Optimization Tags , , , ,

    In this paper, we suggest two ways of calculating interpolation models for unconstrained smooth nonlinear optimization when Hessian-vector products are available. The main idea is to interpolate the objective function using a quadratic on a set of points around the current one and concurrently using the curvature information from products of the Hessian times appropriate … Read more

    Bilevel Derivative-Free Optimization and its Application to Robust Optimization

  • Andrew R. Conn
  • Luis Nunes Vicente
    • Categories Nonlinear Optimization Tags , , , , ,

    We address bilevel programming problems when the derivatives of both the upper and the lower level objective functions are unavailable. The core algorithms used for both levels are trust-region interpolation-based methods, using minimum Frobenius norm quadratic models when the number of points is smaller than the number of basis components. We take advantage of the … Read more