For a project I need something solved, it screams linear programming. If I get the problem in "standard" form I should be able to solve it using the simplex method. But I don't see how to get it in standard form. The problem is this:

Maximize $$min(f_1(\lambda),...,f_p(\lambda))$$ s.t $\sum \lambda_i=1,\lambda_i \geq 0$

where $\lambda=(\lambda_1,...,\lambda_n)$ and $f_i$ linear.

Help or direction to a good source would be much appreciated!


This is a basic case of optimiation problem easy to be cast as a linear one, you can find it in any textbook.

$\max t$

$ t\leq f_i(\lambda),\quad i=1...$

$\sum \lambda_i = 1$

$\lambda_i\geq 0, \quad i=1...$

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    $\begingroup$ This is now the top result for the Google search 'maximize minimum of linear functions'. It's feels a bit condescending to read that one should search carefully before trying to find an answer in SE. $\endgroup$ – JiK Jun 14 '17 at 5:36
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    $\begingroup$ Well, when I wrote the answer it was not....I found things like 4er.org/CourseNotes/Book%20A/A-III.pdf $\endgroup$ – AndreaCassioli Jun 14 '17 at 6:39

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