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

TL;DR

This paper introduces a novel tri-skill variant of the Simplex algorithm with new techniques aimed at achieving a strongly polynomial-time solution for linear programming, addressing a major open problem in the field.

Contribution

It proposes three innovative techniques based on cone-cutting theory and a variable weight optimization method to develop a potentially strongly polynomial-time linear programming algorithm.

Findings

Proposes a tri-skill Simplex variant algorithm.

Introduces a variable weight optimization method.

Suggests a pathway toward strongly polynomial algorithms.

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.