Numerical Optimization

Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

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MMOR Mathematical Methods of Operations Research, 2001: "The books looks very suitable to be used in an graduate-level course in optimization for students in mathematics, operations research, engineering, and others. Moreover, it seems to be very helpful to do some self-studies in optimization, to complete own knowledge and can be a source of new ideas... I recommend this excellent book to everyone who is interested in optimization problems."

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Preface.-Preface to the Second Edition.-Introduction.-Fundamentals of Unconstrained Optimization.-Line Search Methods.-Trust-Region Methods.-Conjugate Gradient Methods.-Quasi-Newton Methods.-Large-Scale Unconstrained Optimization.-Calculating Derivatives.-Derivative-Free Optimization.-Least-Squares Problems.-Nonlinear Equations.-Theory of Constrained Optimization.-Linear Programming: The Simplex Method.-Linear Programming: Interior-Point Methods.-Fundamentals of Algorithms for Nonlinear Constrained Optimization.-Quadratic Programming.-Penalty and Augmented Lagrangian Methods.-Sequential Quadratic Programming.-Interior-Point Methods for Nonlinear Programming.-Background Material.- Regularization Procedure.

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