[Ipopt] Which optimizer is best for an optimization problem with one variable being constrained by the rest variables?

[Peng Yu]

Hi,

I have the following problem.

min f(x), where x satisfies x_n > g(x_1, x_2,...,x_{n-1})

f(x) takes -Inf on the line of x_n = g(x_1, x_2,...,x_{n-1}) and is
undefined when x_n < g(x_1, x_2,...,x_{n-1}).

f is infinitely differentiable in the region of x_n > g(x_1,
x_2,...,x_{n-1}). g is also infinitely differentiable in R^{n-1}.

Does anybody know what the best optimizer is for this problem? Thanks.

-- 
Regards,
Peng