local and superlinear convergence

Non-asymptotic superlinear convergence of Nesterov accelerated BFGS

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

    In this paper, we derive the explicit finite time local convergence of Nesterov accelerated the Broyden-Fletcher-Goldfarb-Shanno (NA-BFGS) under the assumption that the objective function is strongly convex, its gradient is Lipschitz continuous, and its Hessian is Lipschitz continuous at the optimal point. We have shown that the rate of convergence of the NA-BFGS method is … 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