Agent skill

casadi-ipopt-nlp

Nonlinear optimization with CasADi and IPOPT solver. Use when building and solving NLP problems: defining symbolic variables, adding nonlinear constraints, setting solver options, handling multiple initializations, and extracting solutions. Covers power systems optimization patterns including per-unit scaling and complex number formulations.

View SKILL.md on GitHub Repository
Stars 897
Forks 232

Install this agent skill to your Project

npx add-skill https://github.com/benchflow-ai/skillsbench/tree/main/tasks/energy-ac-optimal-power-flow/environment/skills/casadi-ipopt-nlp

SKILL.md

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)

bash
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

python
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:

python
# 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:

python
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

python
# 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

python
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"])

IPOPT options (tuning guide)

Option Default Recommendation Notes
tol 1e-8 1e-7 Convergence tolerance
acceptable_tol 1e-6 1e-5 Fallback if tol not reached
max_iter 3000 2000 Increase for hard problems
mu_strategy monotone adaptive Better for nonconvex
print_level 5 0 Quiet output

Initialization matters

Nonlinear solvers are sensitive to starting points. Use multiple initializations:

python
initializations = [x0_from_data, x0_flat_start]
best_sol = None

for x0 in initializations:
    try:
        sol = solver(x0=x0, lbx=lbx, ubx=ubx, lbg=lbg, ubg=ubg)
        if best_sol is None or float(sol["f"]) < float(best_sol["f"]):
            best_sol = sol
    except Exception:
        continue

if best_sol is None:
    raise RuntimeError("Solver failed from all initializations")

Good initialization strategies:

  • Data-derived: Use values from input data, clipped to bounds
  • Flat start: Nominal values (e.g., Vm=1.0, Va=0.0)
  • Always enforce known constraints in initial point (e.g., reference angle = 0)

Extracting solutions

python
x_opt = np.array(sol["x"]).flatten()

# Unpack by slicing (must match variable order)
Vm_sol = x_opt[:n_bus]
Va_sol = x_opt[n_bus:2*n_bus]
Pg_sol = x_opt[2*n_bus:2*n_bus+n_gen]
Qg_sol = x_opt[2*n_bus+n_gen:]

Power systems patterns

Per-unit scaling

Work in per-unit internally, convert for output:

python
baseMVA = 100.0
Pg_pu = Pg_MW / baseMVA      # Input conversion
Pg_MW = Pg_pu * baseMVA      # Output conversion

Cost functions often expect MW, not per-unit - check the formulation.

Bus ID mapping

Power system bus numbers may not be contiguous:

python
bus_id_to_idx = {int(bus[i, 0]): i for i in range(n_bus)}
gen_bus_idx = bus_id_to_idx[int(gen_row[0])]

Aggregating per-bus quantities

python
Pg_bus = [ca.MX(0) for _ in range(n_bus)]
for k in range(n_gen):
    bus_idx = gen_bus_idx[k]
    Pg_bus[bus_idx] += Pg[k]

Common failure modes

  • Infeasible: Check bound consistency, constraint signs, unit conversions
  • Slow convergence: Try different initialization, relax tolerances temporarily
  • Wrong tap handling: MATPOWER uses tap=0 to mean 1.0, not zero
  • Angle units: Data often in degrees, solver needs radians
  • Shunt signs: Check convention for Gs (conductance) vs Bs (susceptance)
  • Over-rounding outputs: Keep high precision (≥6 decimals) in results

Recommended Agent Skills

Expand your agent's capabilities with these related and highly-rated skills.

benchflow-ai/skillsbench

csv-processing

Use this skill when reading sensor data from CSV files, writing simulation results to CSV, processing time-series data with pandas, or handling missing values in datasets.

897 232
Explore
benchflow-ai/skillsbench

pid-controller

Use this skill when implementing PID control loops for adaptive cruise control, vehicle speed regulation, throttle/brake management, or any feedback control system requiring proportional-integral-derivative control.

897 232
Explore
benchflow-ai/skillsbench

yaml-config

Use this skill when reading or writing YAML configuration files, loading vehicle parameters, or handling config file parsing with proper error handling.

897 232
Explore
benchflow-ai/skillsbench

simulation-metrics

Use this skill when calculating control system performance metrics such as rise time, overshoot percentage, steady-state error, or settling time for evaluating simulation results.

897 232
Explore
benchflow-ai/skillsbench

vehicle-dynamics

Use this skill when simulating vehicle motion, calculating safe following distances, time-to-collision, speed/position updates, or implementing vehicle state machines for cruise control modes.

897 232
Explore
benchflow-ai/skillsbench

web-interface-guidelines

Vercel's comprehensive UI guidelines for building accessible, performant web interfaces. Use this skill when reviewing or building UI components for compliance with best practices around accessibility, performance, animations, and visual stability.

897 232
Explore

Didn't find tool you were looking for?

Be as detailed as possible for better results