Implementing SOCP Constraints Using Python
AnsweredHello,
I've been reading the documentation, and searching the forum (apologies if I've missed it), but am not sure how to correctly implement an SOCP constraint in Gurobi using the Python interface. Here is the problem:
$$\begin{align} \min\limits_{x} q^T x \\ \text{s.t.} \quad &||Dx|| \leq c^{T} x \\ &0 \leq x_i \; \forall i = 1, \ldots, n\end{align}$$
x is an n-dimensional variable input using addMVar
q, D, c are all known (D is p.s.d.)
I attempted to follow this post: https://groups.google.com/forum/#!topic/gurobi/UlCbvUjCs_w . Any help would be greatly appreciated. Thanks!
-ari
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Gurobi Staff
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Hi Ari,
We can do this by introducing an auxiliary n-dimensional MVar \( u = Dx \) and a nonnegative one-dimensional MVar \( y = c^\top x \). Then, we add the constraint \( u^\top u \leq y^2 \). For example:
import gurobipy as gp
import numpy as np
m = gp.Model()
x = m.addMVar(3, name="x")
u = m.addMVar(3, lb=-gp.GRB.INFINITY, name="u")
y = m.addMVar(1, name="y")
D = np.array([[2,-1,0],[-1,2,-1],[0,-1,2]])
c = np.array([1, 2, 3])
m.addConstr(u == D @ x)
m.addConstr(y == c @ x)
m.addConstr(u @ u <= y @ y)I hope this helps!
Eli
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Thank you so much for the help!!
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