Barrier Function improvement

[LockedFlysher]

def penalty(constraint, alpha=0.1, sigma=5, transition_width=0.2):
    """
    Penalty function using tanh for smooth transition

    Parameters:
    - constraint: constraint value g
    - alpha: penalty parameter
    - sigma: switching point
    - transition_width: transition width, smaller values create steeper transitions
    """

    def safe_log(x):
        x = jnp.clip(x, 1e-10, 1e6)
        return jnp.log(x)

    # Function values for the two branches
    quadratic_barrier = alpha / 2 * (jnp.square((constraint - 2 * sigma) / sigma) - jnp.ones_like(constraint))
    log_barrier = -alpha * safe_log(constraint)
    combined_barrier = quadratic_barrier + log_barrier  # Left-side combination

    # Smooth transition weight (between 0 and 1)
    # When g << σ, weight ≈ 0 (use combined_barrier)
    # When g >> σ, weight ≈ 1 (use log_barrier)
    weight = 0.5 * (1 + jnp.tanh((constraint - sigma) / transition_width))

    # Smooth interpolation
    smooth_result = weight * log_barrier + (1 - weight) * combined_barrier

    return jnp.clip(smooth_result, 0, 1e8)

[lorenzo96-cmd]

Hi @LockedFlysher ,
This looks like a good improvement. Did you have the chance to test it?

[LockedFlysher]

Yes, it also works on H1 and talos example, seems the performance keeps the same as your code, a continuously differentiable function can be achieved.