sequential quadratic programming

Solving Chance-Constrained Problems via a Smooth Sample-Based Nonlinear Approximation

  • James R. Luedtke
  • Alejandra Pena-Ordieres
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , , , ,

    We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated via a differentiable sample average approximation. We provide theoretical statistical guarantees of the approximation, and illustrate empirically that the reformulation can … Read more

    A Dynamic Penalty Parameter Updating Strategy for Matrix-Free Sequential Quadratic Optimization

  • James V. Burke
  • Frank E. Curtis
  • Jiashan Wang
  • Hao Wang
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation of the search direction during each iteration, for which we consider the use of matrix-free methods. In particular, we develop a method … Read more

    A Sequential Algorithm for Solving Nonlinear Optimization Problems with Chance Constraints

  • Frank E. Curtis
  • Victor M. Zavala
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    An algorithm is presented for solving nonlinear optimization problems with chance constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained nonlinear optimization problems that arise in sample average approximations of chance-constrained problems, as well as … Read more

    A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control

  • Moritz Diehl
  • Rien Quirynen
  • Robin Verschueren
  • Mario Zanon
    • Categories Systems governed by Differential Equations Optimization Tags , ,

    Quadratic programs (QP) with an indefinite Hessian matrix arise naturally in some direct optimal control methods, e.g. as subproblems in a sequential quadratic programming (SQP) scheme. Typically, the Hessian is approximated with a positive definite matrix to ensure having a unique solution; such a procedure is called \emph{regularization}. We present a novel regularization method tailored … Read more

    A SQP type method for constrained multiobjective optimization

  • Jörg Fliege
  • A. Ismael F. Vaz
    • Categories Multi-Criteria Optimization, Optimization Software and Modeling Systems Tags ,

    We propose an SQP type method for constrained nonlinear multiobjective optimization. The proposed algorithm maintains a list of nondominated points that is improved both for spread along the Pareto front and optimality by solving singleobjective constrained optimization problems. Under appropriate differentiability assumptions we discuss convergence to local optimal Pareto points. We provide numerical results for … Read more

    On the Performance of SQP Methods for Nonlinear Optimization

  • Philip E. Gill
  • Michael A. Saunders
  • Elizabeth Wong
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark Tags , , ,

    This paper concerns some practical issues associated with the formulation of sequential quadratic programming (SQP) methods for large-scale nonlinear optimization. SQP methods find an approximate solution of a sequence of quadratic programming (QP) subproblems in which a quadratic model of the objective function is minimized subject to the linearized constraints. Extensive numerical results are given … Read more

    A Filter SQP Method: Local Convergence and Numerical Results

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

    The work by Gould, Loh, and Robinson [“A filter method with unified step computation for nonlinear optimization”, SIAM J. Optim., 24 (2014), pp. 175–209] established global convergence of a new filter line search method for finding local first-order solutions to nonlinear and nonconvex constrained optimization problems. A key contribution of that work was that the … Read more

    A Filter Active-Set Algorithm for Ball/Sphere Constrained Optimization Problem

  • Shen Chungen
  • Zhang Lei-Hong
  • Weihong Yang
    • Categories Constrained Nonlinear Optimization Tags , , , , , ,

    In this paper, we propose a filter active-set algorithm for the minimization problem over a product of multiple ball/sphere constraints. By making effective use of the special structure of the ball/sphere constraints, a new limited memory BFGS (L-BFGS) scheme is presented. The new L-BFGS implementation takes advantage of the sparse structure of the Jacobian of … Read more

    Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programs

  • Jérôme Bolte
  • Edouard Pauwels
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , , , , , , ,

    In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques from semi-algebraic geometry and variational analysis –in particular Lojasiewicz inequality– we establish the convergence of sequences generated by this type of schemes to critical points. The … Read more

    A Globally Convergent Stabilized SQP Method: Superlinear Convergence

  • Philip E. Gill
  • Vyacheslav Kungurtsev
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization Tags , , , , , ,

    Regularized and stabilized sequential quadratic programming (SQP) methods are two classes of methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that allows convergence to points satisfying certain second-order KKT conditions (SIAM J. Optim., 23(4):1983–2010, 2013). The method is … Read more