Why does linprog generate a 7D optimal solution for 6D simplex problem

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Thomas Kirven 2019-3-18

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https://ww2.mathworks.cn/matlabcentral/answers/450806-why-does-linprog-generate-a-7d-optimal-solution-for-6d-simplex-problem

关闭： MATLAB Answer Bot 2021-8-20

When running linprog with 6x18 constraint matrix (m=6,n=18) and 6x1 b vector, the "optimal" solution generated has 7 nonzero elements when it should only be 6. Why is this the case? I have my own implementation of simplex which comes up with a different solution (6 as apposed to 7 nonzero entries) but both have the same objective function value when evaluated at the solution point.

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Thomas Kirven 2019-3-20

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Matt J, yep this is the exact code and the solution. Also I checked the solution and it does seem to be correct:

A*linprog(f,[],[],A,b,lb)

gives

which is b.

Thomas Kirven 2019-3-20

编辑：Thomas Kirven 2019-3-20

Thank you very much Mary! I think this makes sense now! A linear combination of vertices on the simplex would totally explain why there are 7 non-zero values. In fact it looks like the solution the interior point comes up with is a linear combination of my independently obtained solution and the matlab dual simplex solution Matt provided. Cool!

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