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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
\[ \mbox{Minimize } c'x \mbox{ such that } {\mathbf Ax} = {\mathbf b} \mbox{ and } {\mathbf G \mathbf x}\,\, \leq_{\mathbf K}\,\, {\mathbf h} \] where the last inequality is generalized, that is, \({\mathbf h}-\mathbf{Gx}\) belongs to the cone \({\mathbf K}\).
ECOS supports the positive orthant \({\mathbf R}_+\), second-order cones \({\mathbf Q}_n\) defined as
\[ {\mathbf Q}_n = \bigl\{ (t,{\mathbf x}) | t >= \lVert{\mathbf x}\rVert_2 \bigr\} \]
with \(t\) a scalar and \({\mathbf x} \in {\mathbf R}_{n-1}\), and the exponential cone \({\mathbf K}_e\) defined as
\[ \mathbf{K}_e = \mbox{closure} \bigl\{ (x,y,z) | exp(x/z) <= y/z, z>0 \bigr\}, \]
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:
\[ {\mathbf K} = {\mathbf R}_+ \times {\mathbf Q}_{n_1} \times \cdots \times {\mathbf Q}_{n_N} \times {\mathbf K}_e \times \cdots \times {\mathbf K}_e. \]
Note that the ECOS C language sources are included here. Changes to the original source are clearly delineated for easy reference.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.