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 |
Questions for Chapter 2 | 40 |
Copyright | |
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active constraints active set method algorithm applied approximation assumption BFGS BFGS method bound column computed Consider constrained optimization constraint problem convex function defined derivatives descent direction described in Section dual equality constraint equations equivalent exact penalty function example exists factors feasible direction feasible point Figure Fletcher follows formula given gives global convergence gradient hence Hessian matrix inequality constraints integer iteration KT point L₁ Lagrange multipliers Lagrangian Lemma line search linear constraints linear programming LP problem Math Newton's method node non-smooth nonlinear programming nonlinear programming problem NSO problems Numerical objective function order sufficient conditions positive definite possible Powell problem minimize Proof quadratic function quadratic programming quasi-Newton method reduced result satisfies second order conditions second order sufficient sequence simplex method SNQP solution solving SQP method steepest descent step subproblem Taylor series Theorem trust region updating variables vector x₁ zero