nonlinear optimization

Global Convergence of General Derivative-Free Trust-Region Algorithms to First and Second Order Critical Points

  • Andrew R. Conn
  • Katya Scheinberg
  • Luis Nunes Vicente
    • Categories Unconstrained Optimization Tags , , ,

    In this paper we prove global convergence for first and second-order stationarity points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of linear or quadratic models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds but, … Read more

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

  • Serge Gratton
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , , , ,

    We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Sartenaer, Toint (2004), and provide significant numerical experience on multilevel test problems. A suitable choice of the algorithm’s parameters is identified on these problems, yielding a very satisfactory compromise between reliability and efficiency. The resulting default algorithm is then compared to alternative … Read more

    Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization

  • Serge Gratton
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , ,

    Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function’s local curvature is incomplete, in the sense that it may be restricted to a fixed set of “test directions” and may not be available at every iteration. It is shown that convergence to local “weak” … Read more

    A Homogeneous Model for Mixed Complementarity Problems over Symmetric Cones

  • Yedong Lin
  • Akiko Yoshise
    • Categories Complementarity and Variational Inequalities, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , , ,

    In this paper, we propose a homogeneous model for solving monotone mixed complementarity problems over symmetric cones, by extending the results in \cite{YOSHISE04} for standard form of the problems. We show that the extended model inherits the following desirable features: (a) A path exists, is bounded and has a trivial starting point without any regularity … Read more

    Knitro: An Integrated Package for Nonlinear Optimization

  • Richard H. Byrd
  • Jorge Nocedal
  • Richard A. Waltz
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems Tags , ,

    This paper describes Knitro 5.0, a C-package for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving large-scale, smooth nonlinear programming problems, and it is also effective for the following special cases: unconstrained optimization, nonlinear systems of equations, … 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

    A generating set search method exploiting curvature and sparsity

  • Lennart Frimannslund
  • Trond Steihaug
    • Categories Unconstrained Optimization Tags , , , ,

    Generating Set Search method are one of the few alternatives for optimising high fidelity functions with numerical noise. These methods are usually only efficient when the number of variables is relatively small. This paper presents a modification to an existing Generating Set Search method, which makes it aware of the sparsity structure of the Hessian. … Read more

    Perturbation analysis of second order programming problems

  • Joseph Frédéric Bonnans
  • Héctor Ramírez
    • Categories Linear, Cone and Semidefinite Programming, Second-Order Cone Programming Tags , , , ,

    We discuss first and second order optimality conditions for nonlinear second-order cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong regularity in terms of second order optimality conditions. Citation Research Report 5293 (August … Read more

    Recursive Trust-Region Methods for Multilevel Nonlinear Optimization (Part I): Global Convergence and Complexity

  • Serge Gratton
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , , , ,

    A class of trust-region methods is presented for solving unconstrained nonlinear and possibly nonconvex discretized optimization problems, like those arising in systems governed by partial differential equations. The algorithms in this class make use of the discretization level as a mean of speeding up the computation of the step. This use is recursive, leading to … Read more

    Optimality Measures for Performance Profiles

  • Elizabeth D. Dolan
  • Jorge Moré
  • Todd S. Munson
    • Categories Nonlinear Optimization Tags ,

    We examine the importance of optimality measures when benchmarking a set of solvers, and show that scaling requirements lead to a convergence test for nonlinearly constrained optimization solvers that uses a mixture of absolute and relative error measures. We demonstrate that this convergence test is well behaved at any point where the constraints satisfy the … Read more