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

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

e.g... [tex]max \ f(x) = ...[/tex] s.t. [tex]x_3 \neq 1[/tex]

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

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