10 Questions
Which of the following is a convex function?
Exponential function: $e^x$, for any $x \in R$
Which function is a concave function?
Entropy function: $-x \log x$ for $x > 0$
Which of the following is an example of a convex function on $R^{m \times n}$?
General affine function: $f(X) = tr(A^TX) + b$
Which of the following functions is strictly convex?
Exponential function: $e^x$, for any $x \in R$
Which of the following functions is a concave function?
Sum of squares: $|x|^2 = x_1^2 + \cdots + x_n^2$
Which of the following best defines a convex function?
A function where the domain is convex and satisfies $f( \theta x + (1 - \theta)y) \leq \theta f(x) + (1 - \theta)f(y)$
Which of the following is an example of a concave function on $R^{n}$?
Logarithm: $log(x)$
Which function is a strictly convex function?
Exponential: $e^x$
Which of the following functions is an example of a convex function on $R^{m\times n}$?
Sum of squares: $|x|^2 = x_1^2 + x_2^2 + ... + x_n^2$
Which of the following is NOT an example of a convex function on $R^{n}$?
Powers: $x^\alpha$ for $\alpha geq 1$ or $\alpha leq 0$
Test your knowledge of convex functions with this quiz covering operations that preserve convexity, constructive convex analysis, perspective and conjugate, and quasiconvexity. Learn about convex, concave, and strictly convex functions, and how to determine their properties.
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