Functions -

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The table below lists all the atomic functions available in CVXPY.
constant \(W \in \mathbf{R}^{o \times p}\)
\(\text{dot product of}\) \(\operatorname{sort}\operatorname{vec}(X) \text{ and}\) \(\operatorname{sort}\operatorname{vec}(W)\)
\(X \in \mathbf{R}^{m \times n}\)
sign depends on \(X\), \(W\)
for \(\min(W) \geq 0\)
\(p \in \mathbf{R}^n_{+}\)
\(x_1^{1/n} \cdots x_n^{1/n}\)
\(x \in \mathbf{R}^n_{+}\)
\(\frac{n}{\frac{1}{x_1} + \cdots + \frac{1}{x_n}}\)
\(x \in \mathbf{R}^n_{+}\)
\((x_1\cdots x_n)^{-1}\)
\(x \in \mathbf{R}^n_+\)
\(\lambda_{\max}(X)\)
\(X \in \mathbf{S}^n\)
\(\lambda_{\min}(X)\)
\(X \in \mathbf{S}^n\)
lambda_sum_largest(X,k)
\(\text{sum of $k$ largest}\) \(\text{eigenvalues of $X$}\)
\(X \in\mathbf{S}^{n}\)
lambda_sum_smallest(X,k)
\(\text{sum of $k$ smallest}\) \(\text{eigenvalues of $X$}\)
\(X \in\mathbf{S}^{n}\)
\(\log \left(\det (X)\right)\)
\(X \in \mathbf{S}^n_+\)
\(\log \left(\sum_{ij}e^{X_{ij}}\right)\)
\(X \in\mathbf{R}^{m \times n}\)
\(x \in \mathbf{R}^n\)
\(\max_{ij}\left\{ X_{ij}\right\}\)
\(X \in\mathbf{R}^{m \times n}\)
\(\frac{1}{m n}\sum_{ij}\left\{ X_{ij}\right\}\)
\(X \in\mathbf{R}^{m \times n}\)
\(\min_{ij}\left\{ X_{ij}\right\}\)
\(X \in\mathbf{R}^{m \times n}\)
\(\left(\sum_k\left(\sum_l\lvert x_{k,l}\rvert^p\right)^{q/p}\right)^{1/q}\)
\(X \in\mathbf{R}^{n \times n}\)
\(\sqrt{\sum_{i} \lvert x_{i} \rvert^2 }\)
\(X \in\mathbf{R}^{n}\)
for \(x_{i} \geq 0\)