Hi I am trying to understand the paper of Schollwoeck (arxiv version: https://arxiv.org/pdf/1008.3477.pdf)

There on p.64 formular 203 he states:

In order to solve this problem, we introduce a Lagrangian multiplier λ, and extremize

\[\langle\psi|H|\psi\rangle - \lambda \langle\psi|\psi\rangle \]

If I remember correctly this however translates into an optimization problem where one wants to min/maximize \(\langle \psi | H | \psi \rangle\) subject to the constraint \(\langle \psi | \psi \rangle = 0\) .

See for example https://en.wikipedia.org/wiki/Lagrange_multiplier.

My question now is, how can I understand the constraint? If it would be something like \(\lambda(\langle \psi | \psi \rangle -1 )\) then I could read it as the normalization constraint but in this form I don't know how to make sense of it. May some brighter person please enlighten me?