Dominique Orban

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

    LANCELOt_simple, a simple interface to LANCELOT B

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

    We describe LANCELOT_simple, an interface to the LANCELOT B nonlinear optimization package within the GALAHAD} library (Gould, Orban, Toint, 2003) which ignores problem structure. The result is an easy-to-use Fortran 90 subroutine, with a small number of intuitively interpretable arguments. However, since structure is ignored, the means of presenting problems to the solver limited and … Read more

    The Squared Slacks Transformation in Nonlinear Programming

  • Paul Armand
  • Dominique Orban
    • Categories Constrained Nonlinear Optimization Tags , ,

    We recall the use of squared slacks used to transform inequality constraints into equalities and several reasons why their introduction may be harmful in many algorithmic frameworks routinely used in nonlinear programming. Numerical examples performed with the sequential quadratic programming method illustrate those reasons. CitationCahier du GERAD G-2007-62, Aug. 2007ArticleDownload View PDF

    Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming

  • Paul Armand
  • Dominique Orban
  • Joël Benoist
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the augmented system gives a primal-dual Newton step and also a step in the barrier parameter. Based on local information and … Read more

    Finding optimal algorithmic parameters using a mesh adaptive direct search

  • Charles Audet
  • Dominique Orban
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , , ,

    The objectives of this paper are twofold; we first demonstrate the flexibility of the mesh adaptive direct search (MADS) in identifying locally optimal algorithmic parameters. This is done by devising a general framework for parameter tuning. The framework makes provision for surrogate objectives. Parameters are sought so as to minimize some measure of performance of … Read more

    Sensitivity of trust-region algorithms on their parameters

  • Nicholas I. M. Gould
  • Dominique Orban
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Bound-constrained Optimization, Unconstrained Optimization Tags , ,

    In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommanded ranges of values for these parameters are … 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

    KNITRO-Direct: A Hybrid Interior Algorithm for Nonlinear Optimization

  • Jose Luis Morales
  • Jorge Nocedal
  • Dominique Orban
  • Richard A. Waltz
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags ,

    A hybrid interior-point method for nonlinear programming is presented. It enjoys the flexibility of switching between a line search based method which computes steps by factoring the primal-dual equations and an iterative method using a conjugate gradient algorithm and globalized by means of trust regions. Steps computed by a direct factorization are always tried first, … Read more

    CUTEr (and SifDec), a Constrained and Unconstrained Testing Environment, revisited

  • Nicholas I. M. Gould
  • Dominique Orban
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Optimization Software Benchmark, Problem Solving Environments Tags , , , ,

    The initial release of CUTE, a widely used testing environment for optimization software was described by Bongartz, Conn, Gould and Toint. The latest version, now known as CUTEr, is presented. New features include reorganisation of the environment to allow simultaneous multi-platform installation, new tools for, and interfaces to, optimization packages, and a considerably simplified and … Read more

    Componentwise fast convergence in the solution of full-rank systems of nonlinear equations

  • Nicholas I. M. Gould
  • Dominique Orban
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , ,

    The asymptotic convergence of parameterized variants of Newton’s method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a term involving the variables and a scalar parameter which is driven to zero as the iteration proceeds. The exact local solutions to the perturbed systems then form a differentiable … Read more