A combination of a Proximity technique and Weighted average for LP Problems

It is well known that, for the majority of large-scale LP problems, only a relatively small percentage of constraints are binding at the optimal solution. Redundancy may occur in the formulation phase of the LP problems and even if it does not alter the optimal solution, it may increase the computational cost and the complexity of the problem. For this reason, many researchers have proposed algorithms for identifying redundant constraints in LP problems and thus reducing the dimension of the problem. The goal of this paper is to present a method that uses a subset of the initial constraints that are considered to be essential for the optimal solution. Thus, a combination of a recently proposed proximity technique, that is based on the proximity of the coefficients of the objective function with the corresponding coefficients of the constraints and of an algorithm that is based on the weighted average of the coefficient of each constraint, takes place. Under the newly proposed method, the numerical results are promising.