Does function linprog by interior point method have crossover process to obtain a basic solution?
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Greetings,
Currently, I am working on a linear programming problem. I used function linprog to solve it. However, I found if I specified either using interior point method or dual simplex method, I would get totally different solutions. The reason is the existence of multiple optimal solutions.
As we know, dual simplex method gives a vertex solution. How about interior point method? If interior point method has crossover process, I should get a vertex solution (basic solution). If it has not, I will get a inner point of the hyperplane of constraints.
Does function linprog by interior point method have crossover process to obtain a basic solution?
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Matt J
2019-2-1
Definitely not if your Matlab version is old enough, in which case the interior-point method offered is presumably the same as what is R2018a calls interior-point-legacy. I draw this conclusion from this test,
f=-[1,1];
A=-f;
b=5;
lb=[0,0];
ub=[1,1]*b;
opts=optimoptions('linprog','Algorithm','interior-point-legacy');
x_ipl=linprog(f,A,b,[],[],lb,ub,opts)
which yields the non-basic solution,
x_ipl =
2.5000
2.5000
With the interior-point algorithm of R2018a, I always seem to get a basic solution, but don't know why.
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Matt J
2019-2-19
编辑:Matt J
2019-2-19
When there are multiple optimal solutions to a linear program there is no way to ensure reproducibility of one solution on a different computer or software version. Such optimization problems are numerically unstable and so there is no way, through algorithm implementation, that you can hope to guarantee a particular output.
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