Express Langrange constraint that an expression*cannot* equal a value

[X89codered89X]

I have an optimization where I'd like to express the idea that some of my parameters cannot equal a certain value

e.g... $$max \ f(x) = ...$$ s.t. $$x_3 \neq 1$$

Is there a standard method to solve this using lagrangian optimization?

Thanks.

 

[pasmith]

What you are doing there is best described as restricting the domain of $f$ rather than putting a constraint on $x$. You just have to extremize $f$ in the ordinary way and reject any maximum which has $x_3 = 1$.

 

[X89codered89X]

Ah that is a good point. I had suspected in practice that I would just have to do a rejection like that, but you also gave tasty frontal-lobe-esque reasoning. Thanks!