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سند علمی

Second Order Behavior of Pattern Search Algorithms

Mark A. Abramson

چکیده

Abstract: Previous analyses of pattern search algorithms for unconstrained and linearly constrained minimization have focused on proving convergence of a subsequence of iterates to a limit point satisfying either directional or first-order necessary conditions for optimality, depending on the smoothness of the objective function in a neighborhood of the limit point. Even though pattern search methods require no derivative information, we are able to prove some limited directional second-order results. Although not as strong as classical second-order necessary conditions, these results are stronger than the first order conditions that many gradient-based methods satisfy. Under fairly mild conditions, we can eliminate from consideration all strict local maximizers and an entire class of saddle points.

اسناد مشابه

  • Second-Order Behavior of Pattern Search

    سند علمی۲۰۰۵SIAM Journal on OptimizationMark A. Abramson

    Previous analyses of pattern search algorithms for unconstrained and linearly constrained minimization have focused on proving convergence of a subsequence of iterates to a limit point satisfying either directional or first-order necessary conditions for optimality, depending on

  • Rank Ordering and Positive Bases in Pattern Search Algorithms

    سند علمی۱۹۹۶ROBERT MICHAEL LEWIS

    Abstract. We present two new classes of pattern search algorithms for unconstrained minimization: the rank ordered and the positive basis pattern search methods. These algorithms can nearly halve the worst case cost of an iteration compared to the classical pattern search algorit

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    سند علمی۱۹۹۸J. A. Nelder

    variables may bedevil pattern search methods if there is a high degree of nonlinearity. On the other hand, pattern search methods have been applied successfully to problems with as many as 256 variables. Mead simplex method to a non-stationary point. Direct search methods for unc

  • Pattern Search Algorithms for Surface Wave Analysis

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    In recent years Rayleigh waves have been used increasingly as a nondestructive tool to obtain near-surface S-wave velocity, one of the key parameters in environmental and engineering applications (Miller et al., 1999a, 1999b; Park et al., 1998, 1999; Xia et al., 1999, 2003; Foti

  • From Evolutionary Operation to Parallel Direct Search: Pattern Search Algorithms for Numerical Optimization

    سند علمی۱۹۹۸Virginia Torczon, Michael W. Trosset

    G.E.P. Box’s seminal suggestions for Evolutionary Operation led other statisticians to propose algorithms for numerical optimization that rely exclusively on the direct comparison of function values. These contributions culminated in the development of the widely used simplex alg

  • Precision Control for Generalized Pattern Search Algorithms with Adaptive Precision Function Evaluations

    سند علمی۲۰۰۶SIAM Journal on OptimizationElijah Polak, Michael Wetter

    In the literature on generalized pattern search algorithms, convergence to a stationary point of a once continuously differentiable cost function is established under the assumption that the cost function can be evaluated exactly. However, there is a large class of engineering pr