Tri-skill variant Simplex and strongly polynomial-time algorithm for linear programming

Abstract

The existence of strongly polynomial-time algorithm for linear programming is a cross-century international mathematical problem, whose breakthrough will solve a major theoretical crisis for the development of artificial intelligence. In order to make it happen, this paper proposes three solving techniques based on the cone-cutting theory: 1. The principle of Highest Selection; 2. The algorithm of column elimination, which is more convenient and effective than the Ye-column elimination theorem; 3. A step-down algorithm for a feasible point horizontally shifts to the center and then falls down to the bottom of the feasible region $D$. There will be a nice work combining three techniques, the tri-skill is variant Simplex algorithm to be expected to help readers building the strong polynomial algorithms. Besides, a variable weight optimization method is proposed in the paper, which opens a new window to bring the linear programming into uncomplicated calculation.