global convergence

On the Global Convergence of a Trust Region Method for Solving Nonlinear Constraints Infeasibility Problem

  • Choong Ming Chin
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    A framework for proving global convergence for a class of nonlinear constraints infeasibility problem is presented without assuming that the Jacobian has full rank everywhere. The underlying method is based on the simple sufficient reduction criteria where trial points are accepted provided there is a sufficient decrease in the constraints violation function. The proposed methods … Read more

    GLOBAL CONVERGENCE OF AN ELASTIC MODE APPROACH FOR A CLASS OF MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Mechanical Engineering Tags , , ,

    We prove that any accumulation point of an elastic mode approach, applied to the optimization of a mixed P variational inequality, that approximately solves the relaxed subproblems is a C-stationary point of the problem of optimizing a parametric mixed P variational inequality. If, in addition, the accumulation point satis es the MPCC-LICQ constraint quali cation and if … Read more

    Additional properties of shifted valiable metric methods.

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Unconstrained Optimization Tags , , , ,

    Some supplements to shifted variable metric or quasi-Newton methods for unconstrained minimization are given, including new limited-memory methods. Global convergence of these methods can be established for convex sufficiently smooth functions. Some encouraging numerical experience is reported. Citation Report No. V899-03, Institute of Computer Scienc, Czech Academy of Sciences, Prague, December 2003 (revised May 2004). … Read more

    A Homogeneous Model for $ and *$ Nonlinear Complementarity Problems

  • Akiko Yoshise
    • Categories Complementarity and Variational Inequalities Tags , , ,

    The homogeneous model for linear programs is an elegant means of obtaining the solution or certificate of infeasibility and has importance regardless of the method used for solving the problem, interior-point methods or other methods. In 1999, Andersen and Ye generalized this model to monotone complementarity problems (CPs) and showed that most of the desirable … Read more

    A hybrid algorithm for nonlinear equality constrained optimization problems: global and local convergence theory

  • Mohammedi El Hallabi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Robust Optimization Tags , , , , , , ,

    In this paper we combine both trust-region and linesearch globalization strategies in a globally convergent hybrid algorithm to solve a continuously differentiable nonlinear equality constrained minimization problem. First, the trust-region approach is used to determine a descent direction of the augmented Lagrangian chosen as the merit function, and second, linesearch techniques are used to obtain … Read more

    A Global Convergence Theory of a Filter Line Search Method for Nonlinear Programming

  • Choong Ming Chin
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    A framework for proving global convergence for a class of line search filter type methods for nonlinear programming is presented. The underlying method is based on the dominance concept of multiobjective optimization where trial points are accepted provided there is a sufficient decrease in the objective function or constraints violation function. The proposed methods solve … Read more

    A Simple Primal-Dual Feasible Interior-Point Methodfor Nonlinear Programming with Monotone Descent

  • Sasan Bakhtiari
  • André L. Tits
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    We propose and analyze a primal-dual interior point method of the “feasible” type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of better steering the constructed sequence away from non-KKT stationary … Read more

    On the superlinear local convergence of a filter-SQP method

  • Stefan Ulbrich
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by Fletcher, Leyffer, and Toint [8]. Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function … Read more

    A globally convergent primal-dual interior-point filter method for nonlinear programming

  • Michael Ulbrich
  • Stefan Ulbrich
  • Luis Nunes Vicente
    • Categories Nonlinear Optimization Tags , , ,

    In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primal-dual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, … Read more

    Space mapping: Models, sensitivities, and trust-regions methods

  • Luis Nunes Vicente
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , , ,

    The goal of this paper is to organize some of the mathematical and algorithmic aspects of the recently proposed space-mapping technique for continuous optimization with expensive function evaluations. First, we consider the mapping from the fine space to the coarse space when the models are vector-valued functions and when the space-mapping (nonlinear) least-squares residual is … Read more