# 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

$\mbox{Minimize } c'x \mbox{ such that } Ax = b \mbox{ and } Gx <=_K h$ where the last inequality is generalized, that is, $$h-Gx$$ belongs to the cone $$K$$.

ECOS supports the positive orthant $${\mathbf R}_+$$, second-order cones $$Q_n$$ defined as

$Q_n = \bigl\{ (t,{\mathbf x}) | t >= \lVert{\mathbf x}\rVert_2 \bigr\}$

with $$t$$ a scalar and $${\mathbf x} \in {\mathbf R}_{n-1}$$, and the exponential cone $$K_e$$ defined as

$K_e = \mbox{closure} \bigl\{ (x,y,z) | exp(x/z) <= y/z, z>0 \bigr\},$

where $$(x,y,z) \in {\mathbf R}^3$$.

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

$\begin{array}{l} K = R_+ \times Q_{n_1} \times \cdots \times Q_{n_N} \times K_e \times \cdots \times K_e. \end{array}$

## Further Details

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