An introduction to optimization
An up-to-date, accessible introduction to an increasingly important field This timely and authoritative book fills a growing need for an introductory text to optimization methods and theory at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked-out examples to illustrate both theory and algorithms, this book also provides: A review of the required mathematical background material A mathematical discussion at a level accessible to MBA and business students A treatment of both linear and nonlinear programming An introduction to the most recent developments, including neural networks, genetic algorithms, and the nonsimplex method of Karmarkar A chapter on the use of descent algorithms for the training of feedforward neural networks Exercise problems after every chapter MATLAB exercises and examples An optional solutions manual with MATLAB source listings This book helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business.
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1 Methods of Proof and Some Notation
4 J Concepts from Geometry
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augmented matrix basic columns basic feasible solution basis canonical augmented matrix chromosomes compute Consider constrained optimization problem constraints convex function convex set corresponding crossover defined denoted discuss dual duality equations equivalent example Exercise exists extreme point f(xik feasible direction feasible point feasible set Fibonacci Figure FONC formula genetic algorithm given global minimizer gradient algorithm Hence Hessian Hessian matrix hyperplane inequality input iteration Karmarkar's algorithm Khachiyan's Lagrange condition Lemma level set line search linear programming problem linearly independent LP problem MATLAB maximize neural network neuron Newton's method nonnegative nonsingular norm Note objective function objective function value obtain orthogonal output positive definite primal problem in standard Proof pseudoinverse quadratic function rank satisfies scalar secant method sequence simplex algorithm simplex method solving standard form steepest descent steepest descent algorithm subject to Ax subspace Suppose symmetric Theorem unconstrained update vector xTQx