sequential quadratic programming

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

    Steering Exact Penalty Methods for Optimization

  • Richard H. Byrd
  • Jorge Nocedal
  • Richard A. Waltz
    • Categories Nonlinear Optimization Tags ,

    This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be … Read more

    ON USING THE ELASTIC MODE IN NONLINEAR PROGRAMMING APPROACHES TO MATHEMATICALPROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

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

    We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sucient conditions for their Lagrange multiplier set to be nonempty. MPCCs that have nonempty Lagrange multiplier sets and that satisfy the quadratic growth condition can … Read more

    Constrained optimization in seismic reflection tomography: an SQP augmented Lagrangian approach

  • Frederic Delbos
  • Jean Charles Gilbert
  • R. Glowinski
  • D. Sinoquet
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Quadratic Programming Tags , , , , , ,

    Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a nonlinear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori … Read more

    A sequential quadratic programming algorithm with a piecewise linear merit function

  • Francisco Gomes
    • Categories Constrained Nonlinear Optimization Tags , ,

    A sequential quadratic programming algorithm for solving nonlinear programming problems is presented. The new feature of the algorithm is related to the definition of the merit function. Instead of using one penalty parameter per iteration and increasing it as the algorithm progresses, we suggest that a new point is to be accepted if it stays … Read more

    On an Approximation of the Hessian of the Lagrangian

  • Florian Jarre
    • Categories Constrained Nonlinear Optimization, Optimization Software Design Principles Tags , ,

    In the context of SQP methods or, more recently, of sequential semidefinite programming methods, it is common practice to construct a positive semidefinite approximation of the Hessian of the Lagrangian. The Hessian of the augmented Lagrangian is a suitable approximation as it maintains local superlinear convergence under appropriate assumptions. In this note we give a … Read more

    A robust SQP method for mathematical programs with linear complementarity constraints

  • Xinwei Liu
  • Georgia Perakis
  • Jie Sun
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    The relationship between the mathematical program with linear complementarity constraints (MPCC) and its inequality relaxation is studied. A new sequential quadratic programming (SQP) method is presented for solving the MPCC based on this relationship. A certain SQP technique is introduced to deal with the possible infeasibility of quadratic programming subproblems. Global convergence results are derived … Read more

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

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

    In this paper the theory of local convergence for a class of line search filter type methods for nonlinear programming is presented. The algorithm presented here is globally convergent (see Chin [4]) and the rate of convergence is two-step superlinear. The proposed algorithm solves a sequence of quadratic progrmming subproblems to obtain search directions and … 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

    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