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This is a medium difficulty Machine Learning question, commonly asked during Technical Screen rounds at Uber.

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This question is commonly asked for Machine Learning Engineer candidates at Uber during technical interviews.

Implement convex minimization on an interval

Last updated: May 1, 2026

Quick Overview

This question evaluates understanding of convex optimization for black-box real-valued functions on a closed interval, testing algorithm selection, stopping criteria, time/space complexity, function-evaluation efficiency, and numerical robustness in handling flat regions and boundary optima.

Uber

Aug 10, 2025, 12:00 AM

Machine Learning Engineer

Technical Screen

Machine Learning

Task: Minimize a Black-Box Convex Function on [a, b] Using Only Function Evaluations

Context

You are given a real-valued, convex function F(x) defined on a closed interval [a, b]. The function is a black box: you can evaluate F(x) at chosen x but cannot access derivatives or internal structure.

Requirements

Implement in Python an algorithm to find x* ∈ [a, b] that minimizes F(x), using only function evaluations. Specifically:

Choose and justify an appropriate method (e.g., golden-section search or ternary search).
Specify stopping criteria (tolerance and maximum iterations).
Analyze time and space complexity and the number of function evaluations.
Discuss handling of:
- Numerical precision
- Non-strict convexity and flat regions
- Boundary optima
Provide clear, well-documented code.
Explain how you would test and verify correctness.

Solution

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