Podcast
Play an AI-generated podcast conversation about this lesson
Questions and Answers
Which of the following is a convex function?
Which of the following is a convex function?
- Logarithm function: $log(x)$, for any $x > 0$
- Powers of absolute value: $|x|^p$, for $p \geq 1$
- Negative part function: $min\{0, x\}$
- Exponential function: $e^x$, for any $x \in R$ (correct)
Which function is a concave function?
Which function is a concave function?
- Sum of squares function: $\|x\|^2 = x_1^2 + \cdots + x_n^2$
- Entropy function: $-x \log x$ for $x > 0$ (correct)
- Affine function: $ax + b$, for any $a, b \in R$
- Powers function: $x^\alpha$, for $0 \leq \alpha \leq 1$
Which of the following is an example of a convex function on $R^{m \times n}$?
Which of the following is an example of a convex function on $R^{m \times n}$?
- Sum of squares: $\|x\|^2 = x_1^2 + \cdots + x_n^2$
- Softmax or log-sum-exp function: $log(exp(x_1) + \cdots + exp(x_n))$
- General affine function: $f(X) = tr(A^TX) + b$ (correct)
- Max function: $max(x) = max\{x_1, x_2, \ldots, x_n\}$
Which of the following functions is strictly convex?
Which of the following functions is strictly convex?
Signup and view all the answers
Which of the following functions is a concave function?
Which of the following functions is a concave function?
Signup and view all the answers
Which of the following best defines a convex function?
Which of the following best defines a convex function?
Signup and view all the answers
Which of the following is an example of a concave function on $R^{n}$?
Which of the following is an example of a concave function on $R^{n}$?
Signup and view all the answers
Which function is a strictly convex function?
Which function is a strictly convex function?
Signup and view all the answers
Which of the following functions is an example of a convex function on $R^{m\times n}$?
Which of the following functions is an example of a convex function on $R^{m\times n}$?
Signup and view all the answers
Which of the following is NOT an example of a convex function on $R^{n}$?
Which of the following is NOT an example of a convex function on $R^{n}$?
Signup and view all the answers
