Practical Methods of Optimization: Unconstrained optimization, Volume 1

a₁ Academic Press algorithm applied Applns approximation arise BFGS formula BFGS method Broyden family Broyden method calculated Chebyquad column Computer conjugate gradient methods data fitting problems Davidenko path defined descent direction descent property efficient eigenvalues errors estimate evaluated exact line searches example factors Figure Fletcher follows function f(x Gauss-Newton method given gives global convergence global solution hence Hessian matrix invariant iteration Jacobian matrix least squares Levenberg-Marquardt linear system Maths matrix G method with line modification Newton Newton-Raphson method Newton's method no-derivative numerical orthogonal parameters positive definite possible Powell practice proof quadratic function quadratic model quasi-Newton condition quasi-Newton methods Question rate of convergence requires restricted step method satisfies secant method second derivative Section simplex stationary point steepest descent steepest descent direction system of equations Table theorem trajectory type of method updating formula values variable metric vector Verify x₁ zero