Unconstrained Optimization

Intermediate Report on the development of an optimization code for smooth, high computing load, continuous objective functions when derivatives are not available

  • Frank Vanden Berghen
    • Categories Multidisciplinary Design Optimization, Unconstrained Optimization Tags ,

    We find very often in the industry simulators of huge chemical reactors, simulators of huge turbo-compressors, simulators of the path of a satellite in low orbit around earth, … These simulators were written to allow the design engineer to correctly estimate the consequences of the adjustment of one (or many) design variables (or parameters of … Read more

    The continuous Newton-Raphson method can look ahead

  • Raphael Hauser
  • Jelena Nedic
    • Categories Unconstrained Optimization Tags , , ,

    This paper is about an intriguing property of the continuous Newton-Raphson method for the minimization of a continuous objective function f: if x is a point in the domain of attraction of a strict local minimizer x* then the flux line of the Newton-Raphson flow that starts in x approaches x* from a direction that … Read more

    A Wide Interval for Efficient Self-Scaling Quasi-Newton Algorithms

  • Mehiddin Al-Baali
  • H. Khalfan
    • Categories Unconstrained Optimization Tags , , ,

    This paper uses certain conditions for the global and superlinear convergence of the two-parameter self-scaling Broyden family of quasi-Newton algorithms for unconstraiend optimization to derive a wide interval for self-scaling updates. Numerical testing shows that such algorithms not only accelerate the convergence of the (unscaled) methods from the so-called convex class, but increase their chances … Read more

    A DC piecewise affine model and a bundling technique in nonconvex nonsmooth minimization

  • Antonio Fuduli
  • Manlio Gaudioso
  • Giovanni Giallombardo
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , ,

    We introduce an algorithm to minimize a function of several variables with no convexity nor smoothness assumptions. The main peculiarity of our approach is the use of an the objective function model which is the difference of two piecewise affine convex functions. Bundling and trust region concepts are embedded into the algorithm. Convergence of the … Read more

    New Variable Metric Methods for Unconstrained Minimization Covering the Large-Scale Case

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

    A new family of numerically efficient variable metric or quasi-Newton methods for unconstrained minimization are given, which give simple possibility of adaptation for large-scale optimization. Global convergence of the methods can be established for convex sufficiently smooth functions. Some encouraging numerical experience is reported. CitationReport V876, Institute of Computer Science, AV CR, Pod Vodarenskou Vezi … Read more

    The Trust Region Subproblem and Semidefinite Programming

  • Charles Fortin
  • Henry Wolkowicz
    • Categories Convex Optimization, Semi-definite Programming, Unconstrained Optimization Tags , , ,

    The trust region subproblem (the minimization of a quadratic objective subject to one quadratic constraint and denoted TRS) has many applications in diverse areas, e.g. function minimization, sequential quadratic programming, regularization, ridge regression, and discrete optimization. In particular, it determines the step in trust region algorithms for function minimization. Trust region algorithms are popular for … Read more

    Minimizing nonconvex nonsmooth functions via cutting planes and proximity control

  • Antonio Fuduli
  • Manlio Gaudioso
  • Giovanni Giallombardo
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , ,

    We describe an extension of the classical cutting plane algorithm to tackle the unconstrained minimization of a nonconvex, not necessarily differentiable function of several variables. The method is based on the construction of both a lower and an upper polyhedral approximation to the objective function and it is related to the use of the concept … Read more

    Pattern Search Methods for User-Provided Points:Application to Molecular Geometry Problems

  • Pedro Alberto
  • Luis Nunes Vicente
  • Fernando Nogueira
  • Humberto Rocha
    • Categories Basic Sciences Applications, Unconstrained Optimization Tags , , , , ,

    This paper deals with the application of pattern search methods to the numerical solution of a class of molecular geometry problems with important applications in molecular physics and chemistry. The goal is to find a configuration of a cluster or a molecule with minimum total energy. The minimization problems in this class of geometry molecular … Read more

    A Comparative Study of Large-Scale Nonlinear Optimization Algorithms

  • Hande Benson
  • David F. Shanno
  • Robert J. Vanderbei
    • Categories Constrained Nonlinear Optimization, Quadratic Programming, Unconstrained Optimization Tags , ,

    In recent years, much work has been done on implementing a variety of algorithms in nonlinear programming software. In this paper, we analyze the performance of several state-of-the-art optimization codes on large-scale nonlinear optimization problems. Extensive numerical results are presented on different classes of problems, and features of each code that make it efficient or … Read more

    Smoothing Method of Multipliers for Sum-Max Problems

  • Michael Zibulevsky
    • Categories Convex Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , ,

    We study nonsmooth unconstrained optimization problem, which includes sum of pairwise maxima of smooth functions. Minimum $l_1$-norm approximation is a particular case of this problem. Combining ideas Lagrange multipliers with smooth approximation of max-type function, we obtain a new kind of nonquadratic augmented Lagrangian. Our approach does not require artificial variables, and preserves sparse structure … Read more