Jie Sun

Quadratic Convergence of a Squared Smoothing Newton Method for Nonsmooth Matrix Equations and Its Applications in Semidefinite Optimization Problems

  • Liqun Qi
  • Jie Sun
  • Defeng Sun
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization, Semi-definite Programming Tags ,

    We study a smoothing Newton method for solving a nonsmooth matrix equation that includes semidefinite programming and the semidefinte complementarity problem as special cases. This method, if specialized for solving semidefinite programs, needs to solve only one linear system per iteration and achieves quadratic convergence under strict complementarity. We also establish quadratic convergence of this … Read more

    A Robust Primal-Dual Interior-Point Algorithm for Nonlinear Programs

  • Xinwei Liu
  • Jie Sun
    • Categories Constrained Nonlinear Optimization Tags , ,

    We present a primal-dual interior-point algorithm of line-search type for nonlinear programs, which uses a new decomposition scheme of sequential quadratic programming. The algorithm can circumvent the convergence difficulties of some existing interior-point methods. Global convergence properties are derived without assuming regularity conditions. The penalty parameter rho in the merit function is updated automatically such … Read more

    Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems

  • Jie Sun
  • Defeng Sun
    • Categories Control Applications, Nonsmooth Optimization Tags , , , , ,

    It is well known that the eigenvalues of a real symmetric matrix are not everywhere differentiable. A classical result of Ky Fan states that each eigenvalue of a symmetric matrix is the difference of two convex functions. This directly implies that the eigenvalues of a symmetric matrix are semismooth everywhere. Based on a very recent … Read more