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

Minimize *c*′*x* such that **A***x* = **b** and **G****x** ≤_{K} **h** where the last inequality is generalized, that is, **h** − **G****x** belongs to the cone **K**.

ECOS supports the positive orthant **R**_{+}, second-order cones **Q**_{n} defined as

**Q**_{n} = {(*t*, **x**)|*t* > = ∥**x**∥_{2}}

with *t* a scalar and **x** ∈ **R**_{n − 1}, and the exponential cone **K**_{e} defined as

**K**_{e} = closure{(*x*, *y*, *z*)|*e**x**p*(*x*/*z*) < = *y*/*z*, *z* > 0},

where (*x*, *y*, *z*) ∈ **R**^{3}.

The cone **K** is therefore a direct product of the positive orthant, second-order, and exponential cones:

**K** = **R**_{+} × **Q**_{n1} × ⋯ × **Q**_{nN} × **K**_{e} × ⋯ × **K**_{e}.

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Further Details

Note that the ECOS C language sources are included here. Changes to the original source are clearly delineated for easy reference.