Numerical optimization.

*(English)*Zbl 0930.65067
Springer Series in Operations Research. New York, NY: Springer. xx, 636 p. (1999).

The main goal of the book is to give a comprehensive description of the most powerful, state-of-the-art techniques for solving optimization problems. Since the currently used algorithms are called to handle problems much larger and complex than in the past, the authors emphasized the large-scale optimization techniques, such as interior-point methods, inexact Newton methods, limited-memory methods, and the role of partially separable functions and automatic differentiation. Other important topics such as trust-region methods, sequential quadratic programming, constrained optimization theory, Newton and quasi-Newton methods, nonlinear least squares and nonlinear equations, the simplex method, penalty and barrier methods for nonlinear programming are detailedly and comprehensively discussed.

The book is addressed in general to the people interested in solving optimization problems, and may be used as a (two-semester) graduated-level course in optimization for the engineering, operations research, computer science, and mathematics departments. The presentation style of the book facilitates the self-study and direct application of practitioners in engineering, basic science, and industry. A typical chapter begins with a non-rigorous discussion of the topic at hand, including figures and diagrams and excluding technical details as far as possible. The algorithms are motivated, analyzed and stated explicitly. The major theoretical results are enclosed and, in many cases, proved in a rigorous fashion. These proofs may be skipped. The examples throughout the book show how practical problems are formulated as optimization problems, and the proposed treatment of the optimization process modelling is light, serving mainly to set the stage for the algorithmic developments. The users of optimization software may address the NEOS Guide at http://www.mcs.anl.gov/otc/Guide/SoftwareGuide/ for the specific software packages and latest changes.

The book is addressed in general to the people interested in solving optimization problems, and may be used as a (two-semester) graduated-level course in optimization for the engineering, operations research, computer science, and mathematics departments. The presentation style of the book facilitates the self-study and direct application of practitioners in engineering, basic science, and industry. A typical chapter begins with a non-rigorous discussion of the topic at hand, including figures and diagrams and excluding technical details as far as possible. The algorithms are motivated, analyzed and stated explicitly. The major theoretical results are enclosed and, in many cases, proved in a rigorous fashion. These proofs may be skipped. The examples throughout the book show how practical problems are formulated as optimization problems, and the proposed treatment of the optimization process modelling is light, serving mainly to set the stage for the algorithmic developments. The users of optimization software may address the NEOS Guide at http://www.mcs.anl.gov/otc/Guide/SoftwareGuide/ for the specific software packages and latest changes.

Reviewer: N.Curteanu (Iaşi)

##### MSC:

65K05 | Numerical mathematical programming methods |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

90C06 | Large-scale problems in mathematical programming |

90C30 | Nonlinear programming |

90C55 | Methods of successive quadratic programming type |

90C53 | Methods of quasi-Newton type |

90C51 | Interior-point methods |

65Kxx | Numerical methods for mathematical programming, optimization and variational techniques |