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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 several test sets, including a set of cycling LP problems, Klee-Mintys problems, randomly generated linear programming (LP) problems, and Netlib benchmark problems. The test result shows that the proposed algorithm is (a) degenerate-tolerance as we expected, and (b) more efficient than Dantzigs algorithm for large size randomly generated LP problems but less efficient for Netlib benchmark problems and small size randomly generated problems in terms of CPU time.
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 mak
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To solve these
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,
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