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for questions involving inequalities, upper and lower bounds.

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Is there relationship between $f\left({\sum_i(\mathbf{v}_i^\top\mathbf{x})^2\lambda_i},\sum_...

Consider the following case. Let $f(a,b) = a + b$, $\lambda_1 = \theta_1 = -1$, $\lambda_2 = \theta_2 = 1$, and $V = U = I_2$. Then, $-2 \leq L_1(\mathbf x) \leq 2$ and $L_2 = 0$. Clearly, there exist …
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