Numerical Methods for Unconstrained Optimization: An Introduction |
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Contents
Preface | 1 |
Line Search Techniques | 53 |
The Steepest Descent and Newton Methods | 82 |
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A-conjugate a₁ ap(k approximation Compute contained in Figure continuous second partial convergence criterion convex set corresponding critical point defined by f(x determined eigenvalues equations Fletcher flow diagram function f ƒ defined Gauss-Newton method Gill given Hence Hessian matrix Householder transformation Hypothesis implementation iteration least squares problem Lemma line search line search procedure methods for unconstrained minimizer of ƒ n x n matrix Newton's method nonlinear normed linear space objective function obtain orthogonal partial derivatives point of ƒ positive definite matrix positive semi-definite PROBLEM ni nf Proof quasi-Newton method R¹ defined real numbers real symmetric replacing satisfies search directions second partial derivatives Section sequence simplex solving steepest descent strictly convex strong global minimizer suitable value Suppose symmetric matrix symmetric positive definite Table unconstrained optimization updating formula V₁ value of ƒ whence zero