In general, the application of the general algorithm for solving linear programming problems on a large scale is not desirable.Many researches develop specific algorithms forthese groups of problems are ongoing. Researchersby usingvarious methodshave introduced variety of algorithms that each of which have their own features. In this thesis, a quasi-Newton limited memory BFGS method is proposed for solving linear programs witha very large number of constraints and a very large number of variables. In this method, referring to the previous researches, an exterior penalty function - an unconstraint optimization problem - is developed. This function is a piecewise quadratic convex function which is equivalent to our primal problem and solving this optimization problem leads to solving primal problem. In previous research, a fast newton algorithm is utilized to solve this function. This method acquires solution of least-2- norm of linear programming. For improving the efficiency of newton method, we used the quasi-Newtonlimited memory BFGS method with the fixed step length to solve super large-scale linear programming problems. Direction of this new algorithm is approximating newton’s direction.For comparing our proposed algorithm with other algorithms, over 250 random linear programming problems with their optimal point and objective function are generated. By comparing numerical results, we find that our proposed new algorithm efficiency is higher than other methods. Computational results for small-scale problems are almost the same with the dual simplex algorithm and Newtonmethod. And for large scale,the proposed quasi-Newton algorithm will solve the problem faster than other methods. Moreover, the CPLEX-Dual software and the Newton algorithm for the problems that they are unable to resolve due to lack of memory error can be solved with great efficiency.
