Bound-constrained Optimization

Numerical Experience with a Recursive Trust-Region Method for Multilevel Nonlinear Optimization

  • Serge Gratton
  • Annick Sartenaer
  • Philippe L. Toint
  • Mélodie Mouffe
  • Dimitri Tomanos
    • Categories Bound-constrained Optimization, Distributed Control, Optimization of Systems modeled by PDEs Tags , , , , ,

    We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Mouffe, Toint, Weber (2008) for bound-constrained nonlinear problems, and provide numerical experience on multilevel test problems. A suitable choice of the algorithm’s parameters is identified on these problems, yielding a satisfactory compromise between reliability and efficiency. The resulting default algorithm is then … Read more

    Constraint propagation on quadratic constraints

  • Ferenc Domes
  • Arnold Neumaier
    • Categories Bound-constrained Optimization, Quadratic Programming Tags , , , , , , , ,

    This paper considers constraint propagation methods for continuous constraint satisfaction problems consisting of linear and quadratic constraints. All methods can be applied after suitable preprocessing to arbitrary algebraic constraints. The basic new techniques consist in eliminating bilinear entries from a quadratic constraint, and solving the resulting separable quadratic constraints by means of a sequence of … Read more

    Pricing with uncertain customer valuations

  • Aurelie Thiele
    • Categories Bound-constrained Optimization, Robust Optimization, Yield Management Tags , ,

    Uncertain demand in pricing problems is often modeled using the sum of a linear price-response function and a zero-mean random variable. In this paper, we argue that the presence of uncertainty motivates the introduction of nonlinearities in the demand as a function of price, both in the risk-neutral and risk-sensitive models. We motivate our analysis … Read more

    Regularization and Preconditioning of KKT Systems Arising in Nonnegative Least-Squares Problems

  • Stefania Bellavia
  • Jacek Gondzio
  • Benedetta Morini
    • Categories Bound-constrained Optimization Tags , , , ,

    A regularized Newton-like method for solving nonnegative least-squares problems is proposed and analysed in this paper. A preconditioner for KKT systems arising in the method is introduced and spectral properties of the preconditioned matrix are analysed. A bound on the condition number of the preconditioned matrix is provided. The bound does not depend on the … Read more

    ASTRAL: An Active Set \inftyhBcTrust-Region Algorithm for Box Constrained Optimization

  • James V. Burke
  • Liang Xu
    • Categories Bound-constrained Optimization Tags , , ,

    An algorithm for solving large-scale nonlinear optimization problems with simple bounds is described. The algorithm is an $\ell_\infty$-norm trust-region method that uses both active set identification techniques as well as limited memory BFGS updating for the Hessian approximation. The trust-region subproblems are solved using primal-dual interior point techniques that exploit the structure of the limited … Read more

    Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems

  • Mario A. T. Figueiredo
  • Stephen Wright
  • Robert Nowak
    • Categories Applications - Science and Engineering, Bound-constrained Optimization Tags ,

    Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared $\ell_2$) error term combined with a sparseness-inducing ($\ell_1$) regularization term.{\it Basis pursuit}, the {\it least absolute shrinkage and selection operator} (LASSO), … Read more

    Developments of NEWUOA for unconstrained minimization without derivatives

  • M.J.D. Powell
    • Categories Bound-constrained Optimization, Unconstrained Optimization Tags , , , , ,

    The NEWUOA software is described briefly, with some numerical results that show good efficiency and accuracy in the unconstrained minimization without derivatives of functions of up to 320 variables. Some preliminary work on an extension of NEWUOA that allows simple bounds on the variables is also described. It suggests a variation of a technique in … Read more

    A Coordinate Gradient Descent Method for Nonsmooth Separable Minimization

  • Paul Tseng
  • Sangwoon Yun
    • Categories Bound-constrained Optimization, Convex and Nonsmooth Optimization Tags

    We consider the problem of minimizing the sum of a smooth function and a separable convex function. This problem includes as special cases bound-constrained optimization and smooth optimization with l_1-regularization. We propose a (block) coordinate gradient descent method for solving this class of nonsmooth separable problems. We establish global convergence and, under a local Lipschitzian … Read more

    A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization

  • Serge Gratton
  • Philippe L. Toint
  • Melissa Weber-Mendonca
  • Mélodie Mouffe
    • Categories Bound-constrained Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    A recursive trust-region method is introduced for the solution of bound-constrained nonlinear nonconvex optimization problems for which a hierarchy of descriptions exists. Typical cases are infinite-dimensional problems for which the levels of the hierarchy correspond to discretization levels, from coarse to fine. The new method uses the infinity norm to define the shape of the … Read more

    Derivative Free Optimization Methods for Optimizing Stirrer Configurations

  • Bulent Karasozen
  • Michael Schaefer
  • Omur Ugur
  • Kerim Yapici
    • Categories Bound-constrained Optimization, Chemical Engineering Tags , , ,

    In this paper a numerical approach for the optimization of stirrer configurations is presented. The methodology is based on a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The flow solver is based on the discretization of the incompressible Navier-Stokes equations by means of a fully conservative finite-volume method … Read more