Numerical Methods for Unconstrained Optimization and Nonlinear Equations
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or 'quasi-Newton' methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems.
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analytic Broyden's method Broyden's update calculate CALL Chapter cheapF Cholesky Cholesky decomposition continuously differentiable convex set decomposition definite secant update derivative descent direction difference discussed driver evaluations example Exercise factorization factsec finite finite-difference Frobenius norm function Gauss-Newton method given gradient Guideline implementation Input Parameters Input-Output Parameters iteration itncount Jacobian Lemma Let f line search linear Lipschitz continuous macheps marstep martaken matrix norm matrix storage minimization problem modules Newton step Newton's method nonlinear equations nonlinear least nonlinear problems nonsingular orthogonal matrix Output Parameters positive definite secant proof q-quadratically q-superlinear QR decomposition quadratic model quasi-Newton quasi-Newton method retcode RETURN from Algorithm rithm satisfy scaling secant approximations secant method Section sequence solution solving stepsize steptol Storage Considerations strategy system of algorithms systems of nonlinear term code termcode Theorem trust region typf unconstrained minimization variable Vf(x Vºf zero