The linearization method for constrained optimization

by B. N. Pshenichnyĭ

Techniques of optimization are applied in many problems in economics, automatic control etc. and a wealth of literature is devoted to the subject. The first computer applications involved linear programming problems with simple structure and comparatively uncomplicated nonlinear problems; these could be solved readily with the computational power of existing machines. Problems of increasing size and nonlinear complexity made it necessary to develop a complete new arsenal of methods for obtaining numerical results in a reasonable time. The Linearization Method is one of the fruits of this research of the last 20 years. It is closely related to Newton's method for solving systems of linear equations, to penalty function methods (and, hence, to methods of nondifferentiable optimization) and to variable metrics. The author of this book is one of the pioneers of this approach - a fact that is not widely known even to specialists. The book provides - for a wide readership including engineers