ﻻ يوجد ملخص باللغة العربية
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.
A double pivot algorithm that combines features of two recently published papers by these authors is proposed. The proposed algorithm is implemented in MATLAB. The MATLAB code is tested, along with a MATLAB implementation of Dantzigs algorithm, for s
This paper discusses the odds problem, proposed by Bruss in 2000, and its variants. A recurrence relation called a dynamic programming (DP) equation is used to find an optimal stopping policy of the odds problem and its variants. In 2013, Buchbinder,
We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime mold Physaru
Column generation is often used to solve multi-commodity flow problems. A program for column generation always includes a module that solves a linear equation. In this paper, we address three major issues in solving linear problem during column gener
In this paper, we develop a new algorithm combining the idea of ``boosting with the first-order algorithm to approximately solve a class of (Integer) Linear programs(LPs) arisen in general resource allocation problems. Not only can this algorithm sol