Introduction to Derivative-free OptimizationThe absence of derivatives, often combined with the presence of noise or lack of smoothness, is a major challenge for optimisation. This book explains how sampling and model techniques are used in derivative-free methods and how these methods are designed to efficiently and rigorously solve optimisation problems. |
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Introduction to Derivative-Free Optimization Andrew R. Conn,Katya Scheinberg,Luis N. Vicente Limited preview - 2009 |
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A-poised A-poisedness absolute value Algorithm 6.3 applied Assumption ball Cauchy Chapter coefficients computed condition number consider constant constraints defined definition derivative-free methods derivative-free optimization derivatives directional direct-search methods error bounds evaluations f xk f(xk finite number first first-order fixed fully linear fully quadratic function f function values Gaussian elimination given global convergence global optimization Hence Hessian infinite inside contraction integer lattices interpolation model interpolation set Lagrange polynomials Lemma linear interpolation Lipschitz continuous matrix minimization minimum Frobenius norm mk(xk model-improvement modified Nelder—Mead method nonlinear nonsingular objective function pivot polynomials poised set poisedness poll step polynomial basis polynomial interpolation positive bases positive spanning set problem proof quadratic models radial basis functions sample points sample set satisfies search step second-order sequence SIAM simplex gradient solution stationary points step size parameter successful iterations sufficient decrease surrogate models Theorem trust-region methods trust-region radius update vector vertices xk+1