## Linear and Nonlinear Optimization: Second EditionProvides 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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Linear and Nonlinear Optimization: Second Edition Igor Griva,Stephen G. Nash,Ariela Sofer Limited preview - 2009 |

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algorithm approximation artiﬁcial variables assume basic feasible solution basic variables basic x1 x2 basis matrix coefﬁcients column compute conjugate-gradient method convergence convex corresponding deﬁned derivatives difﬁcult dual problem duality efﬁcient entering variable entries equality constraints equations example Exercises extreme points f xk f(xk feasible point feasible region ﬁlter ﬁnd ﬁnite ﬁrst ﬁrst-order ﬂow formula function f Gaussian elimination gradient Hence Hessian matrix infeasible interior-point methods iteration Lagrange multipliers Lagrangian line search linear program maximize minimize f minimize f(x Newton’s method node nonbasic variables nonlinear optimization nonnegative null space objective function objective value obtain optimal solution optimality conditions optimization problem positive deﬁnite primal-dual problem minimize Prove quasi-Newton methods ratio test satisﬁes search direction Section semideﬁnite sequence simplex method slack variables solve speciﬁed steepest-descent step length subject to Ax sufﬁcient Taylor series techniques theorem unconstrained update V2 f vector Wolfe condition xk+1 zero