Implement 1D convex minimization in Python

Q: Implement 1D convex minimization in Python

This question evaluates skill in gradient-free 1D convex minimization, black-box numerical optimization, and algorithmic analysis—covering selection of a search strategy, stopping criteria and tolerances, handling noisy or flat evaluations, and estimation of function-evaluation and time/space complexity.

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Question

1D Black-Box Convex Minimization (Gradient-Free)

Task

Implement in Python an algorithm to minimize a 1D convex function F(x) over a closed interval [a, b] when gradients are unavailable and only function evaluations are allowed.

Requirements

Describe the approach (e.g., golden-section search) and why it works for 1D convex functions.
Specify stopping criteria and numerical tolerances.
Analyze the number of function evaluations and time/space complexity.
Explain how to handle noisy evaluations or flat regions.
Provide working code and a brief explanation.

Assumptions

F is convex and unimodal on [a, b].
Function evaluations may be expensive; gradients are unavailable.
Optional: evaluations may be noisy (random noise with zero mean).

Implement 1D convex minimization in Python

1D Black-Box Convex Minimization (Gradient-Free)

Task

Requirements

Assumptions

Solution

Comments (0)

Implement 1D convex minimization in Python

Overview

1D Black-Box Convex Minimization (Gradient-Free)

Task

Requirements

Assumptions

Solution

Comments (0)