Possible bug in MGH problem 11 (mgh11)

While testing the mgh11 function, I noticed that evaluating the residuals at the known optimal point does not give a value close to 0 — the residual norm is around 33, when it should be approximately 0.

I believe the issue is in this line:

@NLexpression(model, F[i = 1:m], exp(-abs(y[i] * m * i * x[2])^x[3] / x[1]) - t[i])

According to the original MGH specification (Moré, Garbow & Hillstrom, 1981), problem #11 (Gulf R&D function) should be:

f_i(x) = exp( -|y_i - x2|^x3 / x1 ) - t_i

with t_i = i/100 and y_i = 25 + (-50ln(t_i))^(2/3), and optimal solution x = (50, 25, 1.5).

The current implementation instead computes abs(y[i] * m * i * x[2]), which:

Uses multiplication instead of subtraction between y[i] and x[2].
Introduces the extra factors m and i, which don't belong in the original formula (y[i] already depends on i through t[i]).

Am I right about this? If so, here is a corrected version of the line:

@NLexpression(model, F[i = 1:m], exp(-abs(y[i] - x[2])^x[3] / x[1]) - t[i])

With this change, I confirmed the residual norm at x* = (50, 25, 1.5) is (near) zero, matching the expected optimum.

Thank you for looking into this.

Start at the mgh11 function and inspect the residual expression shown in the issue. Compare it with the original MGH #11 formula, then evaluate the residual norm at x = (50, 25, 1.5); done means the implementation matches the stated formula and the norm is near zero.

Written by the indexing model from the issue text.