Publisher's Synopsis
The significance and originality of this book derive from its novel approach to those optimization problems in which an active set strategy leads to a finite algorithm, such as linear and quadratic programming or l1 and l approximations. The author investigates the underlying structure of these problems, and describes the methods appropriate to their analysis. These methods involve the extensive use of convex analysis, in conjunction with homotopy methods and approximation theory. The main problem classes treated are those of minimizing polyhedral convex functions and solving convex robust estimation problems.;The polyhedral convex function formulation includes not only linear programming and l1 approximation but also a range of important statistical estimation problems based on ranks, while the robust estimation problem generalises least squares methods. In both cases, significant new algorithmic treatments are developed. The methods expounded here are also applied to certain non-convex, nonlinear problems. For example, a finite algorithm is given for the "errors in variables regression" problem (total approximation problem) in the l1 norm.
