NLopt Python Bindings

Warnings

• gotcha Objective and constraint functions must modify the `grad` array in-place, rather than reassigning it. Operations like `grad = 2*x` will not work as they create a new array; instead, use `grad[:] = 2*x` to overwrite the contents of the existing `grad` array.
  Fix: Ensure that any gradient calculations within your objective or constraint functions modify the `grad` parameter's contents directly using slice assignment (e.g., `grad[:] = ...`) or in-place operations.
• breaking Python version compatibility has changed across releases. As of version 2.10.0, `nlopt` officially supports Python 3.9 and above. Older Python versions (e.g., Python 3.8) were explicitly deprecated in NLopt 2.8.0.
  Fix: Upgrade your Python environment to version 3.9 or newer to ensure compatibility and access to the latest `nlopt` features and bug fixes. Check the `nlopt` PyPI page or GitHub releases for specific `requires_python` information for the version you intend to use.
• gotcha Incorrect or missing gradient information can lead to non-convergence or suboptimal results, especially when using gradient-based algorithms. Many NLopt algorithms expect analytically derived gradients for efficiency and accuracy.
  Fix: If possible, always provide accurate analytical gradients to gradient-based algorithms (e.g., `LD_MMA`, `LD_LBFGS`). If gradients are difficult or impossible to obtain, explicitly choose a derivative-free algorithm (e.g., `LN_COBYLA`, `LN_BOBYQA`). Test your gradient implementations by comparing them against finite-difference approximations.
• gotcha NLopt expects nonlinear inequality constraints to be formulated in the form `h(x) <= 0`. Incorrectly formulating these constraints (e.g., as `h(x) >= 0`) will lead to optimization issues or incorrect results.
  Fix: Always rewrite your inequality constraints to fit the `h(x) <= 0` format. For example, a constraint `g(x) >= C` should be written as `C - g(x) <= 0` in your constraint function.
• deprecated Specific algorithm constants, particularly those for sub-algorithms, may be removed or renamed in different underlying NLopt library versions. For instance, `NLOPT_LD_LBFGS_NOCEDAL` was temporarily removed in versions 2.9.x of the underlying NLopt library (affecting its R bindings `nloptr`) before being reintroduced in 2.10.0. While this specific change might not directly impact Python bindings in the same way, it indicates a potential for algorithm identifiers to change.
  Fix: Always consult the official NLopt documentation or the `nlopt` Python module's attributes (`dir(nlopt)`) for the exact algorithm constants available in your installed version. When upgrading, review the changelog for any mentions of algorithm name changes or removals.

Install

• pip install nlopt Install nlopt

Imports

• nlopt

  import nlopt

• numpy

  import numpy as np

  While older documentation or examples might use 'from numpy import *', 'import numpy as np' is the modern and recommended Python idiom to avoid namespace pollution and improve code readability.

Quickstart

This quickstart demonstrates how to set up and run a constrained minimization problem using NLopt. It defines an objective function and nonlinear inequality constraints, both capable of providing gradients. It then initializes an `nlopt.opt` object with a gradient-based algorithm (`LD_MMA`), sets the objective, bounds, and constraints, and performs the optimization. An example using a derivative-free algorithm (`LN_COBYLA`) is also included to show the common pattern for algorithms that do not utilize gradients.

import nlopt
import numpy as np

# Objective function to minimize: f(x) = sqrt(x[1])
# subject to x[1] >= (a*x[0] + b)**3 and x[1] >= 0
# for a1=2, b1=0, a2=-1, b2=1

def myfunc(x, grad):
    if grad.size > 0:
        grad[0] = 0.0
        grad[1] = 0.5 / np.sqrt(x[1])
    return np.sqrt(x[1])

def myconstraint(x, grad, a, b):
    if grad.size > 0:
        grad[0] = 3 * a * (a * x[0] + b)**2
        grad[1] = -1.0
    return (a * x[0] + b)**3 - x[1]

# Problem dimension
n = 2

# Create an optimizer object
opt = nlopt.opt(nlopt.LD_MMA, n)

# Set minimization objective
opt.set_min_objective(myfunc)

# Set bounds
opt.set_lower_bounds([-float('inf'), 0.0]) # x[1] >= 0

# Add nonlinear inequality constraints (h(x) <= 0)
# Constraint 1: x[1] >= (2*x[0])**3  =>  (2*x[0])**3 - x[1] <= 0
opt.add_inequality_constraint(lambda x, grad: myconstraint(x, grad, 2.0, 0.0), 1e-8)
# Constraint 2: x[1] >= (-1*x[0] + 1)**3 => (-1*x[0] + 1)**3 - x[1] <= 0
opt.add_inequality_constraint(lambda x, grad: myconstraint(x, grad, -1.0, 1.0), 1e-8)

# Set stopping criteria
opt.set_xtol_rel(1e-4)
opt.set_maxeval(1000)

# Initial guess
x0 = np.array([1.234, 5.678])

try:
    x_opt = opt.optimize(x0)
    minf = opt.last_optimum_value()
    result_code = opt.last_optimize_result()
    print(f"Optimized result: x = {x_opt}, f(x) = {minf}, return code: {result_code}")
except nlopt.RunTimeError as e:
    print(f"NLopt failed: {e}")

# Example of using a derivative-free algorithm
opt_df = nlopt.opt(nlopt.LN_COBYLA, n)
opt_df.set_min_objective(myfunc) # Note: grad argument will be empty for derivative-free
opt_df.set_lower_bounds([-float('inf'), 0.0])
opt_df.add_inequality_constraint(lambda x, grad: myconstraint(x, grad, 2.0, 0.0), 1e-8)
opt_df.add_inequality_constraint(lambda x, grad: myconstraint(x, grad, -1.0, 1.0), 1e-8)
opt_df.set_xtol_rel(1e-4)

try:
    x_opt_df = opt_df.optimize(x0)
    minf_df = opt_df.last_optimum_value()
    print(f"Derivative-free result: x = {x_opt_df}, f(x) = {minf_df}")
except nlopt.RunTimeError as e:
    print(f"NLopt (derivative-free) failed: {e}")