【摘要】 本文提出了一个直接处理一般形式线性规划的算法而不需要把问题转化为标准形(即所有约束都是等式约束,所有变量都是非负的)。由于算法的基本思想与单纯形法相同,所以当应用子标准形式的线性规划问题时此算法化为单纯形法。文中证明了算法的有限步终止性,最后还讨论了可行域不存在极点的情形。更多还原

【Abstract】 This paper proposes an algorithm to handle linear programming in the genera] form directly without transforming problem into the standard form (i.e. all constraints are equalities and all variables are nonnegatrve). Since the fundamental idea is the same as in the simplex algorithm, the algorithm reduces to the latter if the problem is given in standard form. It is shown that the algorithm terminates in a finite number of steps. Finally, the case where the feasible region has no extreme point is discussed.更多还原