bfgs quasi-newton method

Quadratic Quasi-Newton Optimization – An Interpolated Hybrid Method

  • Andrew Charneski
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags ,

    We present the Quadratic-Quasi-Newton (QQN) algorithm, a novel optimization method that combines gradient descent and quasi-Newton directions through quadratic interpolation. QQN constructs a parametric path d(t) = t(1 − t)(−∇f) + t 2 d L-BFGS and performs univariate optimization along this path, creating an adaptive interpolation that requires no additional hyperparameters beyond those of its … Read more

    Lagrangian dual interior-point methods for semidefinite programs

  • Mituhiro Fukuda
  • Masakazu Kojima
  • Masayuki Shida
    • Categories Convex Optimization, Second-Order Cone Programming, Semi-definite Programming Tags , , , , , , , ,

    This paper proposes a new predictor-corrector interior-point method for a class of semidefinite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguished features of the method are full use of the BFGS quasi-Newton method in the corrector procedure and an application of the conjugate gradient method with an effective … Read more