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Techniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure and comparatively uncomplicated nonlinear pro- blems: These could be solved readily with the computational power of existing machines, more than 20 years ago. Problems of increasing size and nonlinear complexity made it necessa- ry to develop a complete new arsenal of methods for obtai- ning numerical results in a reasonable time. The lineariza- tion 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 me- thods and to methods of nondifferentiable optimization. It requires the efficient solution of quadratic programming problems and this leads to a connection with conjugate gra- dient methods and variable metrics. This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems.
List of contents
1. Convex and Quadratic Programming.- 1.1 Introduction.- 1.2 Necessary Conditions for a Minimum and Duality.- 1.3 Quadratic Programming Problems.- 2. The Linearization Method.- 2.1 The General Algorithm.- 2.2 Resolution of Systems of Equations and Inequalities.- 2.3 Acceleration of the Convergence of the Linearization Method.- 3. The Discrete Minimax Problem and Algorithms.- 3.1 The Discrete Minimax Problem.- 3.2 The Dual Algorithm for Convex Programming Problems.- 3.3 Algorithms and Examples.- Appendix: Comments on the Literature.- References.
