Embedded Conic Solver in R

R interface to the Embedded COnic Solver (ECOS), an efficient and robust C library for convex problems. Conic and equality constraints can be specified in addition to integer and boolean variable constraints for mixed-integer problems. This R interface is inspired by the python interface and has similar calling conventions.

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

$$ \text{Minimize } \mathbf{c}^\top\mathbf{x} \text{ such that } \mathbf{A}\mathbf{x} = \mathbf{b} \text{ and } \mathbf{G}\mathbf{x} \leq_{\mathbf{K}} \mathbf{h} $$

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:

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

Further Details

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