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[Help-glpk] Re: sensitivity analysis

From: Andrew Makhorin
Subject: [Help-glpk] Re: sensitivity analysis
Date: Sat, 16 Jan 2010 17:55:23 +0300

> I'm looking forward to it. In the example you have given, the
> params are linearly dependent on t -- what if the dependence is
> non-linear?

Non-linear dependence leads to a non-linear program, so in this case
the simplex method cannot be applied.

> When the params (not just rhs, coefs, but also any entry in the
> contraint matrix) depends nonlinearly on scaler t, I wonder if there
> are some efficient algorithms. This problem seems extremely hard,

Harder, but not extremely, because you have only one parameter, so
some one-dimensional methods can be used, even a brute force technique.

>  as
> the set of t that shares the same optimal basis might be many disjoint
> intervals. We might just be satisfied with identifying one particular
> interval of t that contains some initial t_0.

Could you provide an example of the dependence?

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