knitr::opts_chunk$set( collapse = TRUE, comment = "#>", fig.path = "README-" )  # 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.

bnaras/ECOSolveR documentation built on Jan. 24, 2021, 9:37 p.m.