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Suppose you have the solution to the following problem

$$ (1) \ \text{minimize} f(x) \\ \text{subject to} \ Ax = b$$

How do you determine the maximum $\epsilon$ such that the solution to (2)

$$ (2) \ \text{minimize} f(x) \\ \text{subject to} \ Ax = b+\epsilon$$

can be accurately written in terms of the solution of (1) using a Taylor series expansion?

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    I imagine that would depend on what exactly is meant by "accurately".2012-04-26
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    Some more background would help. What do you know about $f$, for example?2012-04-26

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