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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2021
- DOI:
- 10.48550/arXiv.2101.02996
- arXiv:
- arXiv:2101.02996
- Bibcode:
- 2021arXiv210102996W
- Keywords:
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- Mathematics - Optimization and Control