Interior methods for constrained optimization. (English) Zbl 0766.65053

Acta Numerica 1992, 341-407 (1992).
[For the entire collection see Zbl 0745.00007.]
This paper presents a survey and recent developments of the theory and practice of interior methods: A detailed treatment of the theory of classical barrier methods in the convex and nonconvex case is included. For the special case of linear optimization, the structure of several interior methods is described. A special interior method for a linear optimization problem and its complexity analysis are given. The practical success of interior methods depends on efficient linear algebra; the relevant techniques for linear and nonlinear problems are described.
Reviewer: J.Guddat (Berlin)


65K05 Numerical mathematical programming methods
90C25 Convex programming
90C30 Nonlinear programming


Zbl 0745.00007