# ECOSolveR

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:

${\mathbf K} = {\mathbf R}_+ \times {\mathbf Q}_{n_1} \times \cdots \times {\mathbf Q}_{n_N} \times {\mathbf K}_e \times \cdots \times {\mathbf K}_e.$

## Further Details

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