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Methods for nonlinear constraints. (English) Zbl 0548.90058
Nonlinear optimization, Proc. NATO Adv. Res. Inst., Cambridge/Engl. 1981, NATO Conf. Ser., Ser. II, 185-211 (1982).
[For the entire collection see Zbl 0541.00004.]
A brief description of various types of methods for solving nonlinear programming problems is given. Each of these types is assessed in regard to efficiency and reliability, both in practice and in regard to the convergence properties of the method. Special attention is given to the use of an exact $$\ell_ 1$$ penalty function, and a method based on the sequential solution of $$\ell_ 1$$ quadratic programming problems.

##### MSC:
 90C30 Nonlinear programming 49M37 Numerical methods based on nonlinear programming 65K05 Numerical mathematical programming methods 90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming 90C20 Quadratic programming