## Numerical methods for unconstrained optimization: an introduction |

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### Contents

Line Search Techniques | 53 |

The Steepest Descent and Newton Methods | 82 |

Conjugate Direction Methods | 113 |

Copyright | |

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### Common terms and phrases

A-conjugate approximation B(fe Compute a(fe contained in Figure continuous second partial convergence criterion convex set corresponding critical point described determined DFP method directions p(fe eigenvalues exists Fletcher flow diagram following theorem g(fe Gauss-Newton method given global minimizer of/over gradient vector H(fe Hence Hessian matrix Householder transformation Hypothesis if/is implementation iteration least squares problem Lemma limit point line search procedure linearly independent lower triangular matrix n x 1 vector n x n matrix Newton's method nonsingular normed linear space objective function obtain of/at orthogonal p(fe positive definite matrix positive semi-definite procedure contained Proof QUAD quasi-Newton method R1 defined real numbers real symmetric replacing s(fe saddle point satisfies search directions second partial derivatives Section sequence x(fe simplex solving steepest descent strictly convex strong global minimizer sufficiently small suitable value Suppose symmetric matrix symmetric positive definite Table updating formula whence x(fe+i xTAx zero