This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms. As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus. The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting rules, basis update methods, and sensitivity analysis.
Home Page: http://www.springer.com/gp/book/9783319659176
License: BSD 2-Clause "Simplified" License
This repository accompanies Linear Programming Using MATLAB® by Nikolaos Ploskas and Nikolaos Samaras (Springer, 2018).
Download the files as a zip using the green button, or clone the repository to your machine using Git.
Release v1.0 corresponds to the code in the published book, without corrections or updates.
For corrections to the content in the published book, see the file errata.md.
See the file Contributing.md for more information on how you can contribute to this repository.
Hi, a great book first of all. I found an error in the file standard2canonical.m and the corresponding text is also misleading. On page 15 (29/639) it says: "Finally, we remove variable x1 from the objective function and the other constraints.". You forgot to insert the equation for x1 into the other equations as you did in the following example on the same page.
Here's my sloppy implementation (assuming that we just have equality constraints):
function [A, c, b] = standard2canonical0(A, c, b)
[m,~] = size(A);
for i = 1:m
s = find(A(i,:) ~= 0);
s = s(1);
as = A(i,s);
cs = c(s);
As = A(i,:);
bs = b(i);
c = c-cs/as*As';
for j = 1:m
if j == i
A(j,:) = A(j,:)/as;
b(j) = b(j)/as;
else
ajs = A(j,s);
A(j,:) = A(j,:)-ajs/as*As;
b(j) = b(j)-ajs/as*bs;
end
end
c(s) = [];
A(:,s) = [];
end
end
I have two files to test the lib, but just the linprogSolver and ipdipm can return the right solution. so, can you tell me what is going on?
test_LP_MATLAB.txt
run test_LP_MATLAB to plot a figure, change the code in test_LP_lib to use rsa, linprogSolver or ipdipm, the result is different. Why? how to test this algorithms by some data?
test_LP_lib.txt
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