local and superlinear convergence

Non-asymptotic superlinear convergence of Nesterov accelerated BFGS

  • Manish Kumar Sahu
  • Suvendu Pattanaik
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    This paper studies the convergence of a Nesterov accelerated variant of the Broyden-Fletcher-Goldfarb-Shanno (NA-BFGS) quasi-Newton method in the setting where the objective function is strongly convex, its gradient is Lipschitz continuous, and its Hessian is Lipschitz continuous at the optimal point. We demonstrate that similar to the classic BFGS method; the Nesterov accelerated BFGS method … Read more

    Local and superlinear convergence of a primal-dual interior point method for nonlinear semidefinite programming

  • Hiroshi Yabe
  • Hiroshi Yamashita
    • Categories Constrained Nonlinear Optimization, Semi-definite Programming Tags , ,

    In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. We propose primal-dual interior point methods based on the unscaled and scaled Newton methods, which correspond to the AHO, HRVW/KSH/M and NT search directions in linear SDP problems. We analyze local behavior of our proposed methods and show their … Read more