GAMS World Forum

The left-hand side of each constraint shows the two-norm of a vector. See the following link, which will help you transform them. Also, you'll want to use the sqrt() and power() commands in GAMS. Alternatively, you can square both sides and avoid the sqrt() representation. https://mathworld.wolfram....

To verify that it's not your computer, try solving it via the NEOS Optimization Server. There's an 8 hour time limit on jobs (if I recall correctly), and you can't write output files, but you can get the GDX output returned to you!

The reason is because the function is not convex. In standard form for an NLP, it's

x^2 + y^2 - z^2 <= 0

The function has a Hessian that is indefinite, having eigenvalues equal to 1, 1, and -1. Thus, the function is not convex.

The parameters won't change because they are... parameters... unless you modify them within the loop.

As for the variables, just reset their levels to zero to affect a cold start.

For example...

x.l=0;
y.l=0;

Don't bother with Simpson's Rule. Just use either the Left Hand Rule or Right Hand Rule. They're easier to implement and, as the width of the intervals approaches zero, the numerical integration approaches the exact value, anyway. (Just use a very small interval.)

Thank you for the clarification! (I also use GAMS as a "first choice" tool, whenever possible.) I haven't coded any forecast model identification problem, but it's surely possible. It would require hard coding the process (via loops or a similar structure) of altering model parameters, rec...

The easiest way is to break (15) into three constraints, each of which uses a term within the set to impose a lower bound on x. For the second such constraint, instead of a max operator, index the constraint on i.

A similar scheme can be applied for (16).

It may be possible, and I work with GAMS weekly, but it's easier to do in R. Try the forecast package by Hyndman! The R software is free, the package is free, and the techniques are well documented in his text, which is available free online at https://otexts.com/fpp2/ It's worth investigating the a...

Whereas Simpson's Rule or even the Trapezoid Rule are theoretically preferable to the Left Hand Rule or Right Hand Rule, one can just integrate with a higher granularity (i.e., smaller intervals) and use one of the simpler approaches. A "loop" structure works nicely, incrementally adding t...

It's not a conversion. They are alternatives. You need to read the text by Ahuja (1993), read a published article on MTZ constraints, or read one of the articles on MTZ enhancements. The three articles below are a starting point for your research. Laporte, G. (1986). Generalized subtour elimination ...