Convergence properties of algorithms for nonlinear optimization. (English) Zbl 0624.90091

The paper reviews some of the most successful methods for unconstrained, constrained and non-differentiable optimization calculations. The author shows that practical experience and careful consideration of the ingredients of a calculation are vital to the development of successful algorithms. It seems that practical considerations provide the main new ideas and that subsequent theoretical studies yield improvement for the algorithms. The theoretical analysis however, is of prime importance for the understanding and structure of the subject concerned with general algorithms for non-linear optimization.
Reviewer: D. Cusmir


90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming
65K10 Numerical optimization and variational techniques
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
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