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Algorithms for very large nonlinear optimization problems. (English) Zbl 0578.90070
Nonlinear optimization, Proc. NATO Adv. Res. Inst., Cambridge/Engl. 1981, NATO Conf. Ser., Ser. II, 281-292 (1982).
[For the entire collection see Zbl 0541.00004.]
The aim of this paper is to review some efficient ways to solve numerically large scale nonlinear optimization problems. The style is informal and no precise mathematical result is given. Rather, the author points out some facts that are important from the point of view of the user. First, he discusses two points in the problem formulation: the splitting of the variables into linear and nonlinear variables, and the local problem definition as opposed to the global problem definition.
The algorithms for globally defined problems that are considered include branch and bound methods, and algorithms for factorable or separable problems and problems with product terms. Algorithms for locally defined problems include successive linear (or quadratic) programming, and reduced gradient algorithms. The use of algorithms using orthogonal notations is also discussed.
Reviewer: J.F.Bonnans

90C30 Nonlinear programming
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
65K05 Numerical mathematical programming methods
90C06 Large-scale problems in mathematical programming
49M37 Numerical methods based on nonlinear programming