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rm \times from convexity formula
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PhDP committed Apr 16, 2018
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Expand Up @@ -98,7 +98,7 @@ <h1>A crash course in second-order logic</h1>
difficult to define without second-order quantification. Another example is a
fairly important concept in optimization: the convexity of functions.</p>

\[\forall f, x, y, \alpha: Convex(f) \iff f(\alpha \times x + (1 - \alpha) \times y) \leq \alpha \times f(x) + (1 - \alpha) \times f(y)\]
\[\forall f, x, y, \alpha: Convex(f) \iff f(\alpha x + (1 - \alpha) y) \leq \alpha f(x) + (1 - \alpha) f(y)\]

<p>with \(\alpha \in \mathbb{R} \mid 0 \leq \alpha \leq 1\), see <a href="http://www.springer.com/gp/book/9780387303031">Nocedal &amp; Wright
(2006)</a>. What makes this second order is the quantification over \(f\), a
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