What does “subject to” mean in reference to Sigma math notation?

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I understand the first part, but what does the “subject to” part mean?

Help? Couldn’t find anything on google searching “sigma subject to”.

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In this case, it means a constraint on the “min” in the previous problem. You want to find the *x*’s that minimize the sum x0 + x1 + x2 + … + x_(n-1), but you’re only considering candidate options that satisfy the requirement that sum x_i * c_i = S. Other choices for x aren’t allowed.

You are trying to minimize a value “subject to a constraint” / “while being constrained” / “only while this thing is true” . In this example, you are not necessarily trying to find the lowest x in a set; you are trying to find the lowest x that *also* has the property that the x times its corresponding c = S.

If the x’s were [1, 2, 3, 4], the c’s were [1, 2, 4, 3], and S = 12, then the minimum value of x subject to the constraint would be x = 3. x = 1 and x = 2 are smaller x’s, but they don’t satisfy the constraint. x = 4 satisfies the constraint, but it’s not less than x = 3.