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f10w
  • Member for 12 years, 1 month
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20 votes
Accepted

Prove that $a^2+ab+b^2\ge 0$

14 votes

Prove by induction $\sum \frac {1}{2^n} < 1$

13 votes
Accepted

How equality in Fenchel-Young inequality characterizes subdifferential?

9 votes

Prove $\frac{1+a^{2}}{1+b+c^{2}} +\frac{1+b^{2}}{1+c+a^{2}} +\frac{1+c^{2}}{1+a+b^{2}} \geq 2$

8 votes
Accepted

How to establish this inequality: $(1-a)(1-b)(1-c) \geq 8abc$ for $a+b+c=1$?

8 votes

How can it be proved that the geometric mean function is concave?

6 votes
Accepted

Inequality problem, for positive $a,b,c$, if $abc=1$, then $\frac{1}{1+a+b^2}+\frac{1}{1+b+c^2}+\frac{1}{1+c+a^2}\leq1$

5 votes
Accepted

Gradient direction vs Steepest direction

5 votes
Accepted

How to prove the geometric mean is concave?

5 votes

Optimization problem with a bilinear constraint

4 votes

Bhatia—Davis inequality: first recorded occurrence?

4 votes

Prove that $\frac{{x_1}^2+{x_2}^2+\cdots+{x_n}^2}{n}x_1x_2\cdots x_n\le\left(\frac{x_1+x_2+\cdots+x_n}{n}\right)^{n+2}$

4 votes
Accepted

Application of the chain rule to $3$-layers neural network

4 votes
Accepted

Optimization with Constraints using Alternating Direction of Method of Multipliers

4 votes
Accepted

I conjecture this inequality $\sqrt[4]{\frac{(xy+yz+xz)(x^2+y^2+z^2)}{9}}\ge\sqrt[3]{\frac{(x+y)(y+z)(z+x)}{8}}$

4 votes

How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$

4 votes

Condition for quartic polynomial coefficients given at least one real root

3 votes

Let $x,y,z>0$ and $x+y+z=1$, then find the least value of ${{x}\over {2-x}}+{{y}\over {2-y}}+{{z}\over {2-z}}$

3 votes
Accepted

Inequality with sum of numbers

3 votes

What is the most elementary proof of these inequalities?

3 votes
Accepted

Why is one of the KKT conditions the same as one of the constraints?

3 votes

Verify Mean Value Theorem for $\,f\left(x\right)=x^3\,$

3 votes
Accepted

Minimum of $\frac{1}{x+y+z}+\frac{1}{x+y+w}+\frac{1}{x+z+w}-\frac{2}{x+y+z+w}$

3 votes
Accepted

Upper bound on $\displaystyle\sum_{\text{cyc}}\dfrac{a}{a^3+b^2+c}$

3 votes
Accepted

Proof of an inequality involving three numbers $(a,b,c)\gt 0$

3 votes
Accepted

$ab(a^2-b^2)+bc(b^2-c^2)+ac(c^2-a^2)\geq 9.\left[\dfrac{(a-b)(a-c)(b-c)}{ab+ac+bc}\right]a.b.c$

3 votes
Accepted

Upper bound on a function with holder continuous gradient.

3 votes
Accepted

Advance Linear Algebra Textbook Recommendations

3 votes
Accepted

subdifferential of ReLU function composition with affine function

3 votes

Prove Cauchy-Schwarz with AM-GM for three variables