Practical Methods of Optimization, Volume 2Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers revised coverage of basic theory and standard techniques, with updated discussions of line search methods, Newton and quasi-Newton methods, and conjugate direction methods, as well as a comprehensive treatment of restricted step or trust region methods not commonly found in the literature. Also includes recent developments in hybrid methods for nonlinear least squares; an extended discussion of linear programming, with new methods for stable updating of LU factors; and a completely new section on network programming. Chapters include computer subroutines, worked examples, and study questions. |
Contents
Introduction | 3 |
Structure of Methods | 12 |
Newtonlike Methods | 44 |
Copyright | |
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active constraints active set method algorithm approximation assumption BFGS BFGS method bound Broyden calculated column computed conjugate Consider constraint problem convex function defined derivatives descent direction described in Section dual elimination equality constraint equations equivalent exact line searches exact penalty function example exists factors feasible direction feasible point feasible region Figure Fletcher follows formula Gauss-Newton method given gives global convergence gradient hence Hessian matrix implies inequality constraints iteration L₁ Lagrange multipliers Lagrangian least squares Lemma line search linear constraints linear programming LP problem Newton's method node non-smooth nonlinear programming objective function obtained orthogonal penalty function positive definite possible Powell primal problem minimize programming problem Proof quadratic function quasi-Newton method reduced result satisfies second order conditions sequence simplex method solve steepest descent subproblem Taylor series termination Theorem trajectory transformation unconstrained updating vector x₁ zero