Linear and Nonlinear Optimization: Second Edition
Provides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication.
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algorithm approximation assume basic feasible solution basic variables basis matrix Chapter coefficients column compute conjugate-gradient method convergence convex corresponding defined derivatives dual problem duality entering variable entries equality constraints equations example Exercises extreme points f(xk feasible direction feasible point feasible region Figure formula function f gradient guarantee Hence Hessian matrix initial interior-point methods inverse iteration Lagrange multipliers Lagrangian Lemma line search linear program linear system maximize Newton direction Newton’s method node nonbasic variables nonlinear optimization nonnegative nonzero null space objective function objective value obtain optimal solution optimality conditions optimization problem orthogonal penalty positive definite positive-definite matrix primal and dual primal-dual problem minimize f(x Prove quasi-Newton methods ratio test result satisfies search direction Section sequence simplex method solve spanning tree standard form steepest-descent step length subject to Ax Taylor series techniques theorem unconstrained update vector Wolfe condition zero