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Dennis
  • Member for 7 years, 3 months
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3 votes
0 answers
73 views

Prove convexity of $f(x)=\sum_{i=1}^{n}{x_i\ln{x_i}}-\left(\sum_{i=1}^{n}{x_i}\right)\ln\left(\sum_{i=1}^{n}{x_i}\right)$ over $\mathbb{R}_{++}^n$ [duplicate]

3 votes
2 answers
232 views

Prove convexity of $f(x_1,x_2,x_3)=\frac{x_1^2+x_1+1}{x_2+x_3}$ over $\{(x_1,x_2,x_3) : x_2,x_3\gt0\}$

2 votes
1 answer
238 views

Gradient descent converges after $ T \leq O(\log(1/\varepsilon))$ iterations for $f(x)=x^T A x$ where $A$ is positive definite matrix

1 vote
2 answers
105 views

Proving global minimum by lower bound of 2-variable function $f(x,y)=x^4+2x^2y+y^2-4x^2-8x-8y$

1 vote
1 answer
187 views

Proving global minimum by lower bound of 2-variable function $f(x,y)=(x-2y)^4+64xy$

1 vote
0 answers
63 views

Prove that $\{\wedge, \rightarrow\}$ is functionally incomplete

1 vote
1 answer
216 views

Recursive function to convert DNF to negated CNF form

1 vote
1 answer
172 views

Proving global minimum by lower bound of 2-variable functions

1 vote
1 answer
77 views

Prove convexity of split function (linear and quadratic)

0 votes
1 answer
277 views

Minimize $x^2-y^2-z^2$ subject to $x^4+y^4+z^4\leq1$ using KKT Conditions

0 votes
2 answers
123 views

$\sum_{i=1}^{n}{\frac{x_i}{\sqrt{1-x_i}}} \geq \sqrt{\frac{n}{n-1}}$ for $x_i \in \mathbb{R}_{++}$ such that $\sum_{i=1}^{n}{x_i}=1$

0 votes
1 answer
185 views

Convolution of function composition of $2t$

0 votes
1 answer
220 views

Minimum formation sequence length for a logic formula equals number of of subformulas

0 votes
3 answers
77 views

Complete square to show that $(x-2y)^4+64xy+16 \geq 0$

0 votes
1 answer
608 views

Prove that the cardinality of the set of all reflexive relations over $\Bbb N$ is $\mathfrak c$