How do I model that constraint: The sum of consecutive four elements in a vector should be less than 10?

[aileen]

Say a vector x has ten values (decision variables). Objective: Maximize the sum of x. How do I model this constraint: The sum of consecutive four elements in the vector should be less than 10.

[aileen]

You can use the lag and lead operator as in the following example:

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Set i /1*10/; Alias (i,j);
Set iconseq(i,j);
Scalar cnt;

loop(i, for(cnt=0 to 3, iconseq(i,i+cnt) = yes));
display iconseq;

Variable x(i);
Equation e(i);
e(i).. sum(iconseq(i,j), x(i)) =l= 10;

If you want your constraint to interpret "consecutive" in a circular manner, you will have to replace + in the loop-statement by ++ like this:

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loop(i, for(cnt=0 to 3, iconseq(i,i++cnt) = yes));