A quadratic equation gives linear-like behavior that contradict the relative minimum?

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Refer to the below.

  1. Is the red term obtained by plugging in the yellow term to the blue term? If not, how is it obtained?

  2. If yes, consider the following: If we want to minimize the blue term, i.e. a quadratic function in $\lambda$, we should choose the green term which is where the relative(thus global) minimum is obtained. Yet we have (2.24) as a constraint on $\lambda$, we need to check if the green term is smaller than our constraint, i.e. (2.24) (= the yellow term). However, the blue term is always minimised by the green term no matter what, why is it true that somewhere else from the relative minimum gives an even smaller value? (in the last line)

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