Practical Methods of Optimization: Unconstrained optimization, Volume 1

a₁ algorithm applied approximation Aq(k arise BFGS formula BFGS method Broyden family Broyden method calculated chosen conjugate gradient methods Davidenko path defined descent property det(S DFP method eigenvalues evaluated exact line searches example factors Figure Fletcher follows function f(x Gauss-Newton method given gives global convergence global solution golden section search hence Hessian matrix invariant least squares Levenberg-Marquardt linear matrix G method with line minimizer modification Newton Newton-Raphson method Newton's method no-derivative non-linear numerical optimization order necessary conditions orthogonal parameters positive definite possible Powell practice problems proof quadratic function quadratic model quasi-Newton condition quasi-Newton methods Question rank one formula rate of convergence reset restricted step method satisfies secant method second derivatives Section 3.5 sequence simplex solve stationary point steepest descent direction steepest descent method Table Taylor series theorem trajectory updating formula variables vector Verify x₁ zero