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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 cx such that Ax = b and Gx  ≤K  h where the last inequality is generalized, that is, h − Gx belongs to the cone K.

ECOS supports the positive orthant R+, second-order cones Qn defined as

Qn = {(t,x)|t >  = ∥x2}

with t a scalar and x ∈ Rn − 1, and the exponential cone Ke defined as

Ke = closure{(x,y,z)|exp(x/z) <  = y/z, z > 0},

where (x,y,z) ∈ R3.

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

K = R+ × Qn1 × ⋯ × QnN × Ke × ⋯ × Ke.

Further Details

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