Introduction

ABNORMAL_TERMINATION_IN_LNSRCH means the L-BFGS-B optimizer failed during its line-search step. That does not automatically mean SciPy is broken. It usually means the objective function, gradient, scaling, or constraints make it impossible for the optimizer to find a safe step in the current direction.

What the Line Search Is Doing

L-BFGS-B is a gradient-based optimizer. On each iteration, it chooses a search direction and then tries to decide how far to move along that direction. That second part is the line search.

If the algorithm cannot find a step size that improves the objective while respecting its numerical rules, it stops with ABNORMAL_TERMINATION_IN_LNSRCH.

Common reasons include:

• the gradient is wrong
• the objective returns nan or inf
• the function is not smooth enough for a quasi-Newton method
• variables are badly scaled
• bounds force the algorithm into a pathological corner

The First Thing to Check: Objective and Gradient Match

The most common cause is a gradient bug. Even a sign error in one term can make line search fail.

Here is a correct example:

1import numpy as np
2from scipy.optimize import fmin_l_bfgs_b
3
4
5def f(x):
6    value = (x[0] - 3.0) ** 2 + (x[1] + 2.0) ** 2
7    grad = np.array([
8        2.0 * (x[0] - 3.0),
9        2.0 * (x[1] + 2.0),
10    ])
11    return value, grad
12
13
14x0 = np.array([10.0, 10.0])
15result = fmin_l_bfgs_b(f, x0, bounds=[(-20, 20), (-20, 20)])
16print(result[0])
17print(result[1]["warnflag"], result[2])

This converges because the objective is smooth and the gradient is correct.

Now imagine the same function with a broken gradient:

1def bad_f(x):
2    value = (x[0] - 3.0) ** 2 + (x[1] + 2.0) ** 2
3    grad = np.array([
4        -2.0 * (x[0] - 3.0),  # wrong sign
5        2.0 * (x[1] + 2.0),
6    ])
7    return value, grad

That kind of mismatch is exactly the sort of thing that can trigger abnormal termination.

Numerical Stability Matters

Another common issue is scale. If one parameter is around 1e-9 and another is around 1e9, the optimizer sees a distorted landscape. Rescaling the variables or reparameterizing the problem often helps more than tuning optimizer flags.

Also check whether your function ever returns invalid values:

1def safe_log_loss(x):
2    if x[0] <= 0:
3        return np.inf, np.array([np.nan])
4    value = -np.log(x[0])
5    grad = np.array([-1.0 / x[0]])
6    return value, grad

A function like this becomes numerically dangerous near zero. If bounds or the initial guess push the optimizer into invalid regions, line search can fail quickly.

Practical Debugging Steps

Use a short checklist:

1. verify the objective never returns nan or inf in the explored region
2. compare your analytic gradient against finite differences
3. rescale variables so magnitudes are comparable
4. relax overly tight bounds if possible
5. try SciPy minimize with method="L-BFGS-B" for clearer control

A simple finite-difference comparison helps catch gradient bugs:

1import numpy as np
2from scipy.optimize import approx_fprime
3
4
5def value_only(x):
6    return (x[0] - 3.0) ** 2 + (x[1] + 2.0) ** 2
7
8
9x = np.array([1.5, -1.0])
10numeric = approx_fprime(x, value_only, epsilon=1e-8)
11analytic = np.array([2.0 * (x[0] - 3.0), 2.0 * (x[1] + 2.0)])
12
13print("numeric:", numeric)
14print("analytic:", analytic)

If these differ materially, fix the gradient before touching optimizer tolerances.

When To Switch Algorithms

L-BFGS-B assumes a smooth problem with usable gradients. If your objective has discontinuities, many flat regions, or noisy simulation output, a different optimizer may fit better. Sometimes the error is not "how do I tune L-BFGS-B?" but "why am I using a line-search quasi-Newton method on a non-smooth objective?"

Common Pitfalls

The biggest mistake is blaming SciPy before validating the gradient. Most abnormal terminations come from the user-supplied function, not the optimizer implementation.

Another mistake is feeding in raw variables with wildly different scales. Optimizers are not magic; poor conditioning shows up as unstable search behavior.

A third issue is using hard clipping or piecewise logic inside the objective, which can make the function non-differentiable exactly where the optimizer needs smoothness.

Summary

• 'ABNORMAL_TERMINATION_IN_LNSRCH means the line search could not find an acceptable step.'
• The most common cause is a wrong or inconsistent gradient.
• 'nan, inf, bad scaling, and overly tight bounds can also trigger the failure.'
• Compare analytic gradients with finite differences before tuning optimizer parameters.
• If the objective is non-smooth or noisy, consider a different optimization method.