ECOS is a numerical software for solving convex second-order cone programs (SOCPs) of type

min  c'*x
s.t. A*x = b
     G*x <=_K h

where the last inequality is generalized, i.e. h - G*x belongs to the cone K. ECOS supports the positive orthant R_+, second-order cones Q_n defined as

Q_n = { (t,x) | t >= || x ||_2 }

with t a scalar and x in R_{n-1}, and the exponential cone K_e defined as

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

where (x,y,z) is in R_3. The cone K is therefore a direct product of the positive orthant, second-order, and exponential cones:

K = R_+ x Q_n1 x ... x Q_nN x K_e x ... x K_e

Homepage:
https://github.com/embotech/ecos
