Nonlinear Optimization

Elastic-Mode Algorithms for Mathematical Programs with Equilibrium Constraints: Global Convergence and Stationarity Properties

  • Mihai Anitescu
  • Paul Tseng
  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , , ,

    The elastic-mode formulation of the problem of minimizing a nonlinear function subject to equilibrium constraints has appealing local properties in that, for a finite value of the penalty parameter, local solutions satisfying first- and second-order necessary optimality conditions for the original problem are also first- and second-order points of the elastic-mode formulation. Here we study … Read more

    Experimental Datasets from Chemical Thermodynamics

  • Evgenii Rudnyi
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , , ,

    I have been working for quite awhile with the treatment of experimental results in chemical thermodynamics. I have tried to organize my archives and make them available for others. There are several experimental datasets in computer readable format and I hope that they can be used as useful benchmarks for data fitting and nonlinear optimization. … Read more

    Variable metric method for minimization of partially separable nonsmooth functions.

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

    In this report, we propose a new partitioned variable metric method for minimization of nonsmooth partially separable functions. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Computational experiments given confirm efficiency and robustness of the new … Read more

    Local Analysis of the Feasible Primal-Dual Interior-Point Method

  • R. Silva
  • Luis Nunes Vicente
  • J. Soares
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In this paper we analyze the rate of local convergence of the Newton primal-dual interior-point method when the iterates are kept strictly feasible with respect to the inequality constraints. It is shown under the classical conditions that the rate is q-quadratic when the functions associated to the inequality constraints define a locally concave feasible region. … Read more

    On Augmented Lagrangian methods with general lower-level constraints

  • Roberto Andreani
  • Ernesto G. Birgin
  • José Mario Martínez
  • María Laura Schuverdt
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    Augmented Lagrangian methods with general lower-level constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems where the constraints are only of the lower-level type. Two methods of this class are introduced and analyzed. Inexact resolution of the lower-level constrained subproblems is considered. Global convergence is proved … Read more

    Adaptive Barrier Strategies for Nonlinear Interior Methods

  • Jorge Nocedal
  • Richard A. Waltz
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    This paper considers strategies for selecting the barrier parameter at every iteration of an interior-point method for nonlinear programming. Numerical experiments suggest that adaptive choices, such as Mehrotra’s probing procedure, outperform static strategies that hold the barrier parameter fixed until a barrier optimality test is satisfied. A new adaptive strategy is proposed based on the … Read more

    Social Cognitive Maps, Swarm Collective Perception and Distributed Search on Dynamic Landscapes

  • Carlos Fernandes
  • Vitorino Ramos
  • Agostinho C. Rosa
    • Categories Nonlinear Systems and Least-Squares, Parallel Algorithms, Stochastic Approaches Tags , , , ,

    Swarm Intelligence (SI) is the property of a system whereby the collective behaviors of (unsophisticated) entities interacting locally with their environment cause coherent functional global patterns to emerge. SI provides a basis with wich it is possible to explore collective (or distributed) problem solving without centralized control or the provision of a global model. To … Read more

    Varying the Population Size of Artificial Foraging Swarms on Time Varying Landscapes

  • Carlos Fernandes
  • Vitorino Ramos
  • Agostinho C. Rosa
    • Categories Nonlinear Systems and Least-Squares, Parallel Algorithms, Stochastic Approaches Tags , , , , , ,

    Swarm Intelligence (SI) is the property of a system whereby the collective behaviors of (unsophisticated) entities interacting locally with their environment cause coherent functional global patterns to emerge. SI provides a basis with wich it is possible to explore collective (or distributed) problem solving without centralized control or the provision of a global model. In … Read more

    Toward a new DIRECT algorithm. A two-points based sampling method

  • Lakhdar Chiter
    • Categories Global Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    The DIRECT algorithm was motivated by a modification to Lipschitzian optimization. The algorithm begins its search by sampling the objective function at the midpoint of an interval, where this function attains its lowest value, and then divides this interval by trisecting it. One of its weakness is that if a global minimum lies at the … Read more

    NOTE ON PAN’S SECOND-ORDER QUASI-NEWTON UPDATES

  • Pan Pingqi
  • Lei-Hong Zhang
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    This note, attempts to further Pan’s second-order quasi-Newton methods(\cite{panqn}). To complement the numerical implementation, the linear convergence of a rank-one second-order update and the least change property are presented. Citation1,Department of Mathematics, Southeast University, Nanjing, 210096, P.R.China.