Minimize $\frac{1}{2}\sum_{i=1}^p (y_i-x_i)^2$ such that $\sum_{i=1}^p y_i - 1=0$ and $\forall i \in [\![ p ]\!]: -y_i \le 0$ by KKT method
158704
How to minimize $\sum_{i=1}^p (y_i-x_i)^2$ with constraints $\sum_{i=1}^p y_i - 1 =0$ and $\forall i=\overline{1,p}:-y_i \le 0$?
138720
Minimum principle in Hilbert space
40905
Prove $f(\sum^k_{i=1} \alpha_i x_i) \leq \sum^k_{i=1} \alpha_i f(x_i) $ for a convex function f
36374
Exercise 1.6.3 from Alon & Spencer's *The Probabilistic Method*: prove that $Pr[|X-Y| \leq 2] \leq 3 Pr[|X-Y| \leq 1]$ for i.i.d. real RVs $X$ and $Y$
103139
Linear optimization problem.
115850
Minimum of $|ax-by+c|$
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
98662
$P(|X|\ge\lambda a)\ge (1-\lambda)^2a^2$ for $0\le \lambda \le 1$
158863
How to prove $\sum_p p^{-2} < \frac{1}{2}$?
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
60206
Find minimum of $P=\frac{\sqrt{3(2x^2+2x+1)}}{3}+\frac{1}{\sqrt{2x^2+(3-\sqrt{3})x +3}}+\frac{1}{\sqrt{2x^2+(3+\sqrt{3})x +3}}$
62958
Maximize $\mathrm{tr}(Q^TCQ)$ subject to $Q^TQ=I$
36099
Show that $\|f\|^{2}$ attains a minimum value on the interior of $B$
52278
How to solve $\sum_{k=2}^\infty {\frac{1}{k^2-1}}$
106552
Find the sum of $\sum \frac{1}{k^2 - a^2}$ when $0<a<1$
132984
$\sum\limits_{k=0}^{\frac{p-1}2}3^k\binom{p}{k}\equiv 2^p-1\pmod{p^2}$
68848
How to simplify $\sum_{k=1}^nk\cdot k!$