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Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
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it's convex sequence inequality
A sequence $a_0,a_1,\dots,a_n$ of real numbers is called concave if $a_{0}=0$, and for each $0<i<n$, we have $a_i\geq\dfrac{a_{i-1}+a_{i+1}}{2}$.
Find the largest $c(n)$ such that for every concave s …