l1-penalty function

An L1 Elastic Interior-Point Method for Mathematical Programs with Complementarity Constraints

  • Zoumana Coulibaly
  • Dominique Orban
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , , , ,

    We propose an interior-point algorithm based on an elastic formulation of the L1-penalty merit function for mathematical programs with complementarity constraints. The method generalizes that of Gould, Orban and Toint (2003) and naturally converges to a strongly stationary point or delivers a certificate of degeneracy without recourse to second-order intermediate solutions. Remarkably, the method allows … Read more

    A second derivative SQP method: local convergence

  • Nicholas I. M. Gould
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization Tags , , ,

    Gould and Robinson (NAR 08/18, Oxford University Computing Laboratory, 2008) gave global convergence results for a second-derivative SQP method for minimizing the exact $\ell_1$-merit function for a \emph{fixed} value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. … Read more

    A second derivative SQP method: theoretical issues

  • Nicholas I. M. Gould
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be … Read more

    A SECOND DERIVATIVE SQP METHOD WITH IMPOSED DESCENT

  • Nicholas I. M. Gould
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be … Read more

    An interior-point L1-penalty method for nonlinear optimization

  • Nicholas I. M. Gould
  • Dominique Orban
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization Tags , , ,

    A mixed interior/exterior-point method for nonlinear programming is described, that handles constraints by an L1-penalty function. A suitable decomposition of the penalty terms and embedding of the problem into a higher-dimensional setting leads to an equivalent, surprisingly regular, reformulation as a smooth penalty problem only involving inequality constraints. The resulting problem may then be tackled … Read more