如何使用 Python 和 Pyomo 和 Ipopt 获得 Hessian 和 Lagragian 梯度来计算 KKT 矩阵

Question

from pyomo.environ import *
from pyomo.opt import SolverFactory, ProblemFormat
m = ConcreteModel()
m.i = Set(initialize=[1, 2, 3])
init_vals = {1:25E+07, 2:0.0, 3:0.0}
#: Variables
m.x = Var(m.i, initialize=init_vals)
#: Objective
m.oF = Objective(expr=m.x[1]**2 +m.x[2]**2 + m.x[3]**2,
        sense=minimize)
ipopt = SolverFactory('ipopt')
ipopt.solve(m, tee=True)

I want to calculate the KKT matrix using the hessian and gradient of Lagrangian for NLP sensitivity. How can I get those from the result of IPOPT solver... I tried to ipopt.hessian(), But it doesn't give anything. Please give me some help.

Answer 1

I think there is a way to do this with sIPOPT and suffixes (see the sIPOPT documentation) but the easier route might be to use a contributed package to Pyomo called PyNumero. You can find an example of building the KKT matrix and extracting the sensitivities here and you can find installation instructions for PyNumero here