local superlinear convergence

Local Convergence Analysis of an Inexact Trust-Region Method for Nonsmooth Optimization

  • Robert Baraldi
  • Drew P. Kouri
    • Categories Infinite Dimensional Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1–40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. This algorithm has demonstrated … Read more

    Local superlinear convergence of polynomial-time interior-point methods for hyperbolic cone optimization problems

  • Yurii Nesterov
  • Levent Tunçel
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    In this paper, we establish the local superlinear convergence property of some polynomial-time interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the logarithmic homogeneity of self-concordant barrier function, which must have {\em negative curvature}. We propose a new path-following predictor-corrector scheme, which work only … Read more