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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Showing that the infimum is a minimum

Let $V > 0$ and let $\Phi(\cdot)$ be the standard normal CDF. Consider the infimum of $$f(x_1, x_2,x_3, p_1, p_2, p_3) := p_1 \Phi(x_1) + p_2 \Phi(x_2) + p_3 \Phi(x_3)$$ with respect to $x_1, x_2, x_3 …
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