matrix equations

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