Zhijian Lai

Riemannian Interior Point Methods for Constrained Optimization on Manifolds

  • Zhijian Lai
  • Akiko Yoshise
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , ,

    We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method (RIPM), is for solving Riemannian  constrained optimization problems. We establish its local superlinear and quadratic convergence  under the standard assumptions. Moreover, we show its global convergence when it is combined with … Read more

    Completely Positive Factorization by a Riemannian Smoothing Method

  • Zhijian Lai
  • Akiko Yoshise
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    Copositive optimization is a special case of convex conic programming, and it optimizes a linear function over the cone of all completely positive matrices under linear constraints. Copositive optimization provides powerful relaxations of NP-hard quadratic problems or combinatorial problems, but there are still many open problems regarding copositive or completely positive matrices. In this paper, … Read more