generalized newton method

Approximations and Generalized Newton Methods

  • Diethard Klatte
  • Bernd Kummer
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , , , ,

    We study local convergence of generalized Newton methods for both equations and inclusions by using known and new approximations and regularity properties at the solution. Including Kantorovich-type settings, our goal are statements about all (not only some) Newton sequences with appropriate initial points. Our basic tools are results of Klatte-Kummer (2002) and Kummer (1988, 1995), … Read more

    Differentiable exact penalty functions for nonlinear second-order cone programs

  • Ellen H. Fukuda
  • Paulo J. S. Silva
  • Masao Fukushima
    • Categories Nonlinear Optimization, Second-Order Cone Programming Tags , , ,

    We propose a method to solve nonlinear second-order cone programs (SOCPs), based on a continuously differentiable exact penalty function. The construction of the penalty function is given by incorporating a multipliers estimate in the augmented Lagrangian for SOCPs. Under the nondegeneracy assumption and the strong second-order sufficient condition, we show that a generalized Newton method … Read more