zbMATH — the first resource for mathematics

Numerical optimization. Theoretical and practical aspects. Transl. from the French. 2nd reviseded. (English) Zbl 1108.65060
Universitext. Berlin: Springer (ISBN 3-540-35445-X/pbk). xiv, 490 p. (2006).
The first edition of the book is refereed under [Numerical optimization. Theoretical and practical aspects. Transl. from the French. Universitext. Berlin: Springer (2003; Zbl 1014.65045)]. The new one comes with substantial extensions on 70 additional pages. New sections are 6.5: Quadratic programming, 7: A case study: Seismic reflection tomography, 11: Applications of nonsmooth optimization, 12: Computational exercises (nonsmooth optimization).
More realistic application problems are introduced with the emphasis on outlining a typical modelling process in more detail. Some new variants of the bundle method for nonsmooth optimization are studied together with the possibility to run some of the codes under consideration on a classical example. Moreover, the presentation of theoretical results on nonsmooth optimization is reorganized and contains now a new subsection with convergence results.
The book provides an excellent basis for studying optimzation theory and algorithms, especially for nonsmooth optimization. Additional case studies, availability of computer codes, and exercises improve the understanding of numerical algorithms and the practical problem solving process. In summary, the second edition significantly improves the first one.

65K05 Numerical mathematical programming methods
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
90-08 Computational methods for problems pertaining to operations research and mathematical programming
90C05 Linear programming
90C20 Quadratic programming
90C30 Nonlinear programming
90C51 Interior-point methods
Full Text: DOI