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Let $f_1,f_2$ be two smooth quasiconcave functions defined on a convex subset of $\mathbb{R}^d$. It is known that $f_1+f_2$ is not necessarily quasiconcave. Does there always exist monotonically ...

Complementary slackness condition in the KKT theorem states that: $\lambda_i^*\geq0; \lambda_i^*h_i(x^*)=0 $ The usual reasoning goes like this: either constraint is clack $h_i(x^*)>0$ and then ...

A function $f: \mathbb{R} \times \mathbb{R} \to \mathbb{R}$ is supermodular if for every $x'>x$ and $y'>y$, $$f(x',y') + f(x,y) > f(x',y) + f(x,y').$$ Suppose $f$ and $g$ are supermodular, ...