Univariate Minimization Examples

Example Code

Representative script:

"""IMSL UVMIF example: minimize exp(x) - 5x using univariate bounded search.

Reproduces the IMSL UVMIF published example:
- Function: f(x) = exp(x) - 5x
- Starting point: x = 0
- Bound: 100
- Expected minimum at x = ln(5) ≈ 1.609, f ≈ -3.047

Outputs:
- Table printed to stdout
- SVG plot saved to test_output/demo_imsl_uvmif.svg
"""

from __future__ import annotations

from pathlib import Path
from typing import Dict

import matplotlib.pyplot as plt
import numpy as np

from optimization import minimize_univariate


def run_demo_imsl_uvmif() -> Dict[str, object]:
    """Run IMSL UVMIF example: minimize exp(x) - 5x.

    Args:
        None

    Returns:
        Dict[str, object]: Result dict with keys ``x_min`` (float),
            ``fval`` (float), and ``plot_path`` (str).
    """
    def f(x: float) -> float:
        return np.exp(x) - 5.0 * x

    result = minimize_univariate(f, x_guess=0.0, bound=100.0, step=0.1, x_tol=1e-5, max_fev=200)

    x_min = float(result.x[0])
    fval = float(result.fval)

    print("\nIMSL UVMIF Example: minimize exp(x) - 5x")
    print("-" * 45)
    print(f"{'Parameter':<20} {'Value':>15}")
    print("-" * 45)
    print(f"{'x (minimum)':<20} {x_min:>15.6f}")
    print(f"{'f(x)':<20} {fval:>15.6f}")
    print(f"{'ln(5) [exact]':<20} {np.log(5):>15.6f}")
    print(f"{'f(ln5) [exact]':<20} {f(np.log(5)):>15.6f}")
    print(f"{'Converged':<20} {str(result.success):>15}")
    print(f"{'Function evals':<20} {result.n_fev:>15}")
    print("-" * 45)

    output_dir = Path("test_output")
    output_dir.mkdir(parents=True, exist_ok=True)
    plot_path = output_dir / "demo_imsl_uvmif.svg"

    x_vals = np.linspace(-1.0, 4.0, 400)
    y_vals = np.array([f(xi) for xi in x_vals])

    fig, ax = plt.subplots(figsize=(8, 5))
    ax.plot(x_vals, y_vals, color="#1f77b4", linewidth=2.0, label=r"$f(x) = e^x - 5x$")
    ax.axvline(x_min, color="#d62728", linestyle="--", linewidth=1.5, label=f"Minimum x≈{x_min:.4f}")
    ax.scatter([x_min], [fval], color="#d62728", s=60, zorder=5)
    ax.set_xlabel("x")
    ax.set_ylabel("f(x)")
    ax.set_title("IMSL UVMIF: Univariate Bounded Minimization")
    ax.legend()
    ax.grid(True, alpha=0.3)
    fig.tight_layout()
    fig.savefig(plot_path, format="svg")
    plt.close(fig)

    return {"x_min": x_min, "fval": fval, "plot_path": str(plot_path)}


if __name__ == "__main__":
    run_demo_imsl_uvmif()

Input (Console)

Run the univariate minimization script from the package root:

python examples/example_imsl_uvmif.py

Plot Output

Generated SVG plot:

Output Console

Summary console output:

IMSL UVMIF Example: minimize exp(x) - 5x
---------------------------------------------
Parameter                      Value
---------------------------------------------
x (minimum)                 1.609438
f(x)                       -3.047190
ln(5) [exact]               1.609438
f(ln5) [exact]             -3.047190
Converged                       True
Function evals                    20
---------------------------------------------