Primal-dual method for a linear program with hybrid direction

Abstract

In linear programming, the combination of primal and dual methods is of great importance in the search of efficient resolution algorithms. In the present paper, we are interested to the adaptive method with hybrid direction for the linear programs with bounded variables. After calculating the increment of the dual function with this hybrid direction, an optimality criterion for the dual problem is proved. Using this criterion and the initial speed of change for the dual function, a primal-dual algorithm with hybrid direction is suggested for solving linear programs with bounded variables. In this algorithm, the suboptimality estimate is used as a stopping criterion. A numerical example is presented and to compare the suggested method with three other methods, we have developed an implementation under the MATLAB programming language on randomly generated problems with precision ε ≥ 0, chosen in advance.