Nonlinear Optimization

TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities

  • Benedetta Morini
  • Margherita Porcelli
    • Categories Bound-constrained Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares

    The Matlab implementation of a trust-region Gauss-Newton method for bound-constrained nonlinear least-squares problems is presented. The solver, called TRESNEI, is adequate for zero and small-residual problems and handles the solution of nonlinear systems of equalities and inequalities. The structure and the usage of the solver are described and an extensive numerical comparison with functions from … Read more

    A Derivative-Free Algorithm for the Least-square minimization

  • Andrew R. Conn
  • Katya Scheinberg
  • Hongchao Zhang
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , , , ,

    We develop a framework for a class of derivative-free algorithms for the least-squares minimization problem. These algorithms are based on polynomial interpolation models and are designed to take advantages of the problem structure. Under suitable conditions, we establish the global convergence and local quadratic convergence properties of these algorithms. Promising numerical results indicate the algorithm … Read more

    Solving the Sensor Network Localization Problem using an Heuristic Multistage Approach

  • Andrea Cassioli
    • Categories Bound-constrained Optimization, Telecommunications

    The Sensor Network Localization Problem (SNLP), arising from many applied fields related with environmental monitoring, has attracted much research during the last years. Solving the SNLP deals with the reconstruction of a geometrical structure from incomplete pairwise distances between sensors. In this paper we present an heuristic multistage approach in which the solving strategy is … Read more

    A quasisecant method for minimizing nonsmooth functions

  • Adil Bagirov
  • Asef Nazari
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    In this paper a new algorithm to locally minimize nonsmooth, nonconvex functions is developed. We introduce the notion of secants and quasisecants for nonsmooth functions. The quasisecants are applied to find descent directions of locally Lipschitz functions. We design a minimization algorithm which uses quasisecants to find descent directions. We prove that this algorithm converges … Read more

    A practical method for solving large-scale TRS

  • Marianna S. Apostolopoulou
  • C.A. Botsaris
  • Panagiotis Pintelas
  • Dimitris G. Sotiropoulos
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Quadratic Programming Tags , , , , ,

    We present a nearly-exact method for the large scale trust region subproblem (TRS) based on the properties of the minimal-memory BFGS method. Our study in concentrated in the case where the initial BFGS matrix can be any scaled identity matrix. The proposed method is a variant of the Mor\'{e}-Sorensen method that exploits the eigenstructure of … Read more

    Transformations enabling to construct limited-memory Broyden class methods

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

    The Broyden class of quasi-Newton updates for inverse Hessian approximation are transformed to the formal BFGS update, which makes possible to generalize the well-known Nocedal method based on the Strang recurrences to the scaled limited-memory Broyden family, using the same number of stored vectors as for the limited-memory BFGS method. Two variants are given, the … Read more

    Limited-memory projective variable metric methods for unconstrained minimization

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

    A new family of limited-memory variable metric or quasi-Newton methods for unconstrained minimization is given. The methods are based on a positive definite inverse Hessian approximation in the form of the sum of identity matrix and two low rank matrices, obtained by the standard scaled Broyden class update. To reduce the rank of matrices, various … Read more

    Computational experience with modified conjugate gradient methods for unconstrained optimization

  • Ladislav Lukšan
  • Ctirad Matonoha
  • Jan Vlček
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    In this report, several modifications of the nonlinear conjugate gradient method are described and investigated. Theoretical properties of these modifications are proved and their practical performance is demonstrated using extensive numerical experiments. CitationTechnical report No. 1038, Institute of Computer Science, Pod Vodarenskou Vezi 2, 18207 Praha 8. December 2008ArticleDownload View PDF

    Interior-point method for nonlinear programming with complementarity constraints

  • Ladislav Lukšan
  • Ctirad Matonoha
  • Jan Vlček
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , , ,

    In this report, we propose an algorithm for solving nonlinear programming problems with com-plementarity constraints, which is based on the interior-point approach. Main theoretical results concern direction determination and step-length selection. We use an exact penalty function to remove complementarity constraints. Thus a new indefinite linear system is defined with a tridiagonal low-right submatrix. Inexact … Read more

    An adaptive cubic regularisation algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Bound-constrained Optimization, Constrained Nonlinear Optimization Tags , , , , ,

    The adaptive cubic overestimation algorithm described in Cartis, Gould and Toint (2007) is adapted to the problem of minimizing a nonlinear, possibly nonconvex, smooth objective function over a convex domain. Convergence to first-order critical points is shown under standard assumptions, but without any Lipschitz continuity requirement on the objective’s Hessian. A worst-case complexity analysis in … Read more