diagonal quasi-Newton method

An efficient penalty decomposition algorithm for minimization over sparse symmetric sets

  • Ahmad Mousavi
  • Morteza Kimiaei
  • Saman Babaie-Kafaki
  • Vyacheslav Kungurtsev
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems approximately via a two-block decomposition scheme: the first subproblem admits a closed-form solution without sparsity constraints, while the second subproblem is handled through an efficient … Read more

    A class of diagonal quasi-Newton penalty decomposition algorithms for sparse bound-constrained nonconvex optimization

  • Ahmad Mousavi
  • Morteza Kimiaei
  • Saman Babaie-Kafaki
  • Vyacheslav Kungurtsev
    • Categories Bound-constrained Optimization, Constrained Nonlinear Optimization, Quadratic Programming Tags , , ,

    This paper discusses an improved quasi-Newton penalty decomposition algorithm for the cardinality bound-constrained optimization problems whose simple bounds on the variables are assumed to be finite. Until an approximate stationary point is found, this algorithm approximates the solutions of a sequence of penalty subproblems by a two-block decomposition scheme. This scheme finds an approximate solution … Read more