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 c′x 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 > = ∥x∥2}
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.