• Speaker: Prof Levent Tunçel, University of Waterloo
  • Title: Superlinear Convergence of polynomial-time interior-point methods for convex optimization
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 17th Sep 2015
  • Abstract:

    We propose new path-following predictor-corrector algorithms for solving convex optimization problems in conic form. The main structural properties used in our design and analysis of the algorithms hinge on some key properties of a special class of very smooth, strictly convex barrier functions. Even though our analysis has primal and dual components, our algorithms work with the dual iterates only, in the dual space. Our algorithms converge globally at the same worst-case rate as the current best polynomial-time interior-point methods. In addition, our algorithm have the local superlinear convergence property under some mild assumptions. The algorithms are based on an easily computable gradient proximity measure, which ensures an automatic transformation of the global linear rate of convergence to the locally superlinear one under some mild assumptions. Our step-size procedure for the predictor step is related to the maximum step size (the one that takes us to the boundary).

    This talk is based on joint work with Yu. Nesterov.

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