Embedded Conic Solver in R. This is an R wrapper around the ecos project on GitHub which describes ECOS as below.
ECOS is a numerical software for solving convex second-order cone programs (SOCPs) of type
\text{Minimize } \mathbf{c}^\top\mathbf{x} \text{ such that } \mathbf{A}\mathbf{x} = \mathbf{b} \text{ and } \mathbf{G}\mathbf{x} \leq_{\mathbf{K}} \mathbf{h}
where the last inequality is generalized, that is, \mathbf{h} - \mathbf{G}\mathbf{x} belongs to the cone \mathbf{K}.
ECOS supports the positive orthant \mathbf{R}_+, second-order cones \mathbf{Q}_n defined as
\mathbf{Q}_n = \bigl\lbrace (t, \mathbf{x}) \mid t \geq \lVert \mathbf{x} \rVert_2 \bigr\rbrace
with t a scalar and \mathbf{x} \in \mathbf{R}^{n-1}, and the exponential cone \mathbf{K}_e defined as
\mathbf{K}_e = \text{closure} \bigl\lbrace (x, y, z) \mid \exp(x/z) \leq y/z,\ z > 0 \bigr\rbrace,
where (x, y, z) \in \mathbf{R}^3.
The cone \mathbf{K} is therefore a direct product of the positive orthant, second-order, and exponential cones:
\mathbf{K} = \mathbf{R}_+ \times \mathbf{Q}_{n_1} \times \cdots \times \mathbf{Q}_{n_N} \times \mathbf{K}_e \times \cdots \times \mathbf{K}_e.