What is a lagrangian constraint?

It's being used in the context of minimizing the variance of an investment portfolio.

A plain english answer please

Go to the link.

Hope it helps:
It's very easy to minimise (maximise) a function whose second derivative is always positive (negative) by simply obtaining its derivatives and equating them to zero.
If, in addition to that, you need some EQUALITY constraints (for example, constraining the portfolio value to be 1) then, you need the LAGRANGE MMULTIPLIER METHOD.

Say you have min f(X), st.t. g(x)=0
then construct F(X) = f(x)-L g(X), derive ,and solve equating derivatives to zero.
when you derive with respect to L (the lagrange multiplier), you obtain the original restriction: g(x) =0.
Now, typically, in asset managament applications, you need INEQUALITY CONSTRAINTS (For example, only positive holdings)
Then , since the variance is a quadratic form, you need quadratic programming.
Hope it helps

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