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I am interested in the value function of a quadratic program of the form $$ v(y)=\min_x \frac{1}{2} x^\top Q(y) x, $$ subject to a linear equality constraint $$ E(y)x=d(y), $$ and a linear inequality …

Apologies if this question is not appropriate for MathOverflow. I have asked at Math.StackExchange without success. Consider the function $f:\mathbb{R}^n\rightarrow \mathbb{R}$ defined as $$ f(x)=\le …

Consider a polynomial $\sum\limits_{k=0}^n a_kx^k$ with $a_k\geq 0$ and $x\geq 0$. In this comment, Richard Stanley mentions that polynomials with only real roots are log concave functions. Can somebo …

Consider a function $f:\mathbb{R}^n_{\geq 0}\rightarrow \mathbb{R}$ that is separately convex, i.e. such that $\frac{d^2f}{dx_i^2}\geq 0$ for all $i\in \{1,\dots n\}$. Assume also that $f$ is decreasi …