CasADi + IPOPT for Nonlinear Programming

CasADi is a symbolic framework for nonlinear optimization. IPOPT is an interior-point solver for large-scale NLP.

Quick start (Linux)

apt-get update -qq && apt-get install -y -qq libgfortran5
pip install numpy==1.26.4 casadi==3.6.7

Building an NLP

1. Decision variables

import casadi as ca

n_bus, n_gen = 100, 20
Vm = ca.MX.sym("Vm", n_bus)   # Voltage magnitudes
Va = ca.MX.sym("Va", n_bus)   # Voltage angles (radians)
Pg = ca.MX.sym("Pg", n_gen)   # Real power
Qg = ca.MX.sym("Qg", n_gen)   # Reactive power

# Stack into single vector for solver
x = ca.vertcat(Vm, Va, Pg, Qg)

2. Objective function

Build symbolic expression:

# Quadratic cost: sum of c2*P^2 + c1*P + c0
obj = ca.MX(0)
for k in range(n_gen):
    obj += c2[k] * Pg[k]**2 + c1[k] * Pg[k] + c0[k]

3. Constraints

Collect constraints in lists with bounds:

g_expr = []  # Constraint expressions
lbg = []     # Lower bounds
ubg = []     # Upper bounds

# Equality constraint: g(x) = 0
g_expr.append(some_expression)
lbg.append(0.0)
ubg.append(0.0)

# Inequality constraint: g(x) <= limit
g_expr.append(another_expression)
lbg.append(-ca.inf)
ubg.append(limit)

# Two-sided: lo <= g(x) <= hi
g_expr.append(bounded_expression)
lbg.append(lo)
ubg.append(hi)

g = ca.vertcat(*g_expr)

4. Variable bounds

# Stack bounds matching variable order
lbx = np.concatenate([Vm_min, Va_min, Pg_min, Qg_min]).tolist()
ubx = np.concatenate([Vm_max, Va_max, Pg_max, Qg_max]).tolist()

5. Create and call solver

nlp = {"x": x, "f": obj, "g": g}
opts = {
    "ipopt.print_level": 0,
    "ipopt.max_iter": 2000,
    "ipopt.tol": 1e-7,
    "ipopt.acceptable_tol": 1e-5,
    "ipopt.mu_strategy": "adaptive",
    "print_time": False,
}
solver = ca.nlpsol("solver", "ipopt", nlp, opts)

sol = solver(x0=x0, lbx=lbx, ubx=ubx, lbg=lbg, ubg=ubg)
x_opt = np.array(sol["x"]).flatten()
obj_val = float(sol["f"])