cumsum in AMPL

[Hans]

I need to formulate a constraint involving a `cumsum` calculation:

    sum_{k=1}^j (x_k - p_k) <= d  for all j in 1..n

The following expression in AMPL does not work as it returns an error message

"k is not defined":

    subject to some_rule {j in 1..n}: sum {k in 1..j} x[k] - p[k] <= d

How can I write such a constraint in AMPL correctly?

Many thanks in advance.

[Robert Fourer]

As in the mathematical expression, the scope of the "sum" in the AMPL expression ends at the first + or - sign, unless you parenthesize it like this:

subject to some_rule {j in 1..n}: sum {k in 1..j} (x[k] - p[k]) <= d;

Without the parentheses, the sum only extends to x[k], and you get an error message that k is undefined in p[k].

Bob Fourer
am...@googlegroups.com

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