Suppose we have a problem such as:
max f(x) subject to g(x) $\le$ b
where, g(x) is the constraint function
The Lagrange for such a problem could be constructed as follows,
L(x, $\lambda\ $) = f(x) + $\lambda\ $.[b - g(x)]
From complementary slackness, $\lambda$.[b - g(x)] = 0, if the function binds the b-g(x) = 0, if it doesn't then $\lambda\ $ = 0, why is $\lambda$ = 0 if the constraint does not bind and is therefore slack?
Thank you.