A new polynomial-time algorithm for linear programming
Combinatorica
An infeasible (exterior point) simplex algorithm for assignment problems
Mathematical Programming: Series A and B
Multiple centrality corrections in a primal-dual method for linear programming
Computational Optimization and Applications
Combining interior-point and pivoting algorithms for linear programming
Management Science
Introduction to Linear Optimization
Introduction to Linear Optimization
A new efficient primal dual simplex algorithm
Computers and Operations Research
Linear Programming and Network Flows
Linear Programming and Network Flows
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Linear Programming (LP) is a significant research area in the field of operations research. The simplex algorithm is the most widely used and well-studied method for solving Linear Programming problems (LPs). Many algorithms have been proposed for the solution of LPs. The vast majority of these algorithms belong to three main categories: (i) Simplex-type or pivoting algorithms, (ii) interior-point methods (IPMs) and (iii) exterior point simplex type algorithms (EPSA). The aim of this paper is to present an implementation of a hybrid simplex algorithm that begins to solve the LP using an IPM and after a number of iterations continues with a primal-dual EPSA algorithm. This hybrid approach aims to take advantage of: (i) IPM strengths, which is the fast convergence in the first iterations, and (ii) EPSA strengths, i.e. the fast convergence when making steps in directions that are linear combinations of attractive directions. The idea of combining different types of linear programming algorithms is not new; to the best of our knowledge, this is the first time that interior point methods and exterior point algorithms are combined. The interior point that is calculated by IPM after a number of iterations can lead to such attractive directions. In order to gain an insight into the practical behavior of the proposed algorithm, we have performed some computational experiments over sparse randomly generated optimal LPs. Finally, in the computational study that we have conducted, we investigate the adequate number of iterations that IPM should run in order to decrease the CPU time and the iterations of the proposed algorithm.