Takashi Tsuchiya

An extension of the standard polynomial-time primal-dual path-following algorithm to the weighted determinant maximization problem with semidefinite constraints

  • Takashi Tsuchiya
  • Yu Xia
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    The problem of maximizing the sum of linear functional and several weighted logarithmic determinant (logdet) functions under semidefinite constraints is a generalization of the semidefinite programming (SDP) and has a number of applications in statistics and datamining, and other areas of informatics and mathematical sciences. In this paper, we extend the framework of standard primal-dual … Read more

    A strong bound on the integral of the central path curvature and its relationship with the iteration complexity of primal-dual path-following LP algorithms

  • Renato D.C. Monteiro
  • Takashi Tsuchiya
    • Categories Linear Programming, Linear, Cone and Semidefinite Programming Tags , , , , , , , , , , , , ,

    The main goals of this paper are to: i) relate two iteration-complexity bounds associated with the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming (LP), and; ii) study the geometrical structure of the central path in the context of LP. The first forementioned iteration-complexity bound is expressed in terms of an integral introduced by Sonnevend, Stoer and … Read more

    Implementation of Infinite Dimensional Interior Point Method for Solving Multi-criteria Linear-Quadratic Control Problem

  • Leonid Faybusovich
  • Takashi Tsuchiya
  • Thanasak Mouktonglang
    • Categories Control Applications, Infinite Dimensional Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We describe an implementation of an infinite-dimensional primal-dual algorithm based on the Nesterov-Todd direction. Several applications to both continuous and discrete-time multi-criteria linear-quadratic control problems and linear-quadratic control problem with quadratic constraints are described. Numerical results show a very fast convergence (typically, within 3-4 iterations) to optimal solutions Citation Preprint, May, 2004, University of Notre … Read more

    A New Computational Approach to Density Estimation with Semidefinite Programming

  • Tadayoshi Fushiki
  • Takashi Tsuchiya
  • Shingo Horiuchi
    • Categories Data-Mining, Semi-definite Programming, Statistics Tags , , , ,

    Density estimation is a classical and important problem in statistics. The aim of this paper is to develop a new computational approach to density estimation based on semidefinite programming (SDP), a new technology developed in optimization in the last decade. We express a density as the product of a nonnegative polynomial and a base density … Read more

    Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank

  • Leonid Faybusovich
  • Takashi Tsuchiya
    • Categories Control Applications, Linear, Cone and Semidefinite Programming Tags , , , ,

    We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for “infinite-dimensional second-order cone programs.” We consider as an example a … Read more

    Uniform Boundedness of a Preconditioned Normal Matrix Used in Interior Point Methods

  • Renato D.C. Monteiro
  • Takashi Tsuchiya
  • Jerome W. O'Neal
    • Categories Linear Programming, Network Optimization Tags , , , , , , ,

    Solving systems of linear equations with “normal” matrices of the form $A D^2 A^T$ is a key ingredient in the computation of search directions for interior-point algorithms. In this article, we establish that a well-known basis preconditioner for such systems of linear equations produces scaled matrices with uniformly bounded condition numbers as $D$ varies over … Read more

    Optimal Magnetic Shield Design with Second-Order Cone Programming

  • Takashi Sasakawa
  • Takashi Tsuchiya
    • Categories Multidisciplinary Design Optimization, Second-Order Cone Programming Tags , , ,

    In this paper, we consider a continuous version of the convex network flow problem which involves the integral of the Euclidean norm of the flow and its square in the objective function. A discretized version of this problem can be cast as a second-order cone program, for which efficient primal-dual interior-point algorithms have been developed … Read more

    A new iteration-complexity bound for the MTY predictor-corrector algorithm

  • Renato D.C. Monteiro
  • Takashi Tsuchiya
    • Categories Linear, Cone and Semidefinite Programming Tags , ,

    In this paper we present a new iteration-complexity bound for the Mizuno-Todd-Ye predictor-corrector (MTY P-C) primal-dual interior-point algorithm for linear programming. The analysis of the paper is based on the important notion of crossover events introduced by Vavasis and Ye. For a standard form linear program $\min\{c^Tx : Ax=b, \, x \ge 0\}$ with decision … Read more