Global optimization. Deterministic approaches. 3rd rev. a. enl. ed. (English) Zbl 0867.90105

Horst, Reiner; Tuy, Hoang

Berlin: Springer. xviii, 728 p. (1996).

The present edition contains some modifications and additions which take into account recent developments in the field. The most important improvements on the first edition (1990; Zbl 0704.90057) are shortly emphasized in what follows.
Section VIII.5.1 was completed by a new version of a decomposition method for minimum concave cost flow problems which provides a useful bound on the number of iterations in the integer case and which was elaborated by R. Horst and N. V. Thoai.
In Section X.1.2 the outer approximation algorithm for canonical d.c. problems proposed by N. V. Thoai [Optimization 19, No. 5, 665-674 (1988; Zbl 0662.90069)] was replaced by a new stable approach developed by H. Tuy.
In Chapter XI, Section 2.5 on functions with concave minorants was added. In this section, the authors discuss new branch-and-bound methods that provide considerably improved linear programming bounding procedures for diverse problems such as linearly constrained Lipschitz-, d.c.- and Hölder-optimization problems as well as solving systems of nonlinear inequalities. The results given in this new section are based on investigations by R. Horst, M. Nast and N. V. Thoai.
All the modifications that were made are welcome, because they assure that this valuable reference book remains up to date.

Reviewer: W.W.Breckner (Cluj-Napoca)

MSC:

90C30	Nonlinear programming
65K05	Numerical mathematical programming methods
90-02	Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming

Keywords:

outer approximation