Yoshiyuki Sekiguchi

Analytic Formulas for Alternating Projection Sequences for the Positive Semidefinite Cone and an Application to Convergence Analysis

  • Hiroyuki Ochiai
  • Yoshiyuki Sekiguchi
  • Hayato Waki
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , , ,

    \(\) We derive analytic formulas for the alternating projection method applied to the cone \(S^n_+\) of positive semidefinite matrices and an affine subspace. More precisely, we find recursive relations on parameters representing a sequence constructed by the alternating projection method. By applying these formulas, we analyze the alternating projection method in detail and show that … Read more

    Exact Convergence Rates of Alternating Projections for Nontransversal Intersections

  • Hiroyuki Ochiai
  • Yoshiyuki Sekiguchi
  • Hayato Waki
    • Categories Convex Optimization Tags , , , , ,

    We study the exact convergence rate of the alternating projection method for the nontransversal intersection of a semialgebraic set and a linear subspace. If the linear subspace is a line, the exact rates are expressed by multiplicities of the defining polynomials of the semialgebraic set, or related power series. Our methods are also applied to … Read more

    Perturbation Analysis of Singular Semidefinite Program and Its Application to a Control Problem

  • Yoshiyuki Sekiguchi
  • Hayato Waki
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    We consider the sensitivity of semidefinite programs (SDPs) under perturbations. It is well known that the optimal value changes continuously under perturbations on the right hand side in the case where the Slater condition holds in the primal problems. In this manuscript, we observe by investigating a concrete SDP that the optimal value can be … Read more