large-update method

A Comparative Study of New Barrier Functions for Primal-Dual Interior-Point Algorithms in Linear Optimization

  • Y.Q. Bai
  • Cornelis Roos
  • M. Elghami
    • Categories Linear Programming, Linear, Cone and Semidefinite Programming Tags , , , ,

    Recently, so-called self-regular barrier functions for primal-dual interior-point methods (IPMs) for linear optimization were introduced. Each such barrier function is determined by its (univariate) self-regular kernel function. We introduce a new class of kernel functions. The class is defined by some simple conditions on the kernel function and its derivatives. These properties enable us to … Read more

    A New and Efficient Large-Update Interior-Point Method for Linear Optimization

  • Jiming Peng
  • Cornelis Roos
  • Tamás Terlaky
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    Recently, the authors presented a new large-update primal-dual method for Linear Optimization, whose $O(n^\frac23\,\log\frac{n}{\e})$ iteration bound substantially improved the classical bound for such methods, which is $O\br{n\log\frac{n}{\e}}$. In this paper we present an improved analysis of the new method. The analysis uses some new mathematical tools developed before when we considered a whole family of … Read more