Abstract: In this paper two algorithms are proposed based on the method of direct saddlepoint convergence The important valuos of the two algorithms are: ① The new algerithms transform problems of saddlepoint into problems of quadratic extreme value. ② The new algorithms can find optimum value in finite number of steps ③There is a polynomial-time property when solving linear programming problems with the algorithms. ④ The new concept of difference gradient of the saddlepoint is proposed.