Exterior Point Simplex-Type Algorithms for Linear and Network Optimization Problems

摘要

Two decades of research led to the development of a number of efficient algorithms that can be classified as exterior point simplex-type. This type of algorithms can cross over the infeasible region of the primal (dual) problem and find an optimal solution reducing the number of iterations needed. Thus, such approaches aim to find an efficient way to get to an optimal basis via a series of infeasible ones. In this lecture, we present the developments in exterior point simplex-type algorithms for linear and network optimization problems, over the recent years. We also present other approaches that, in a similar way, do not preserve primal or dual feasibility at each iteration such as the monotonic build-up Simplex algorithms and the criss-cross methods, and also discuss some open research problems.