# Compare L1 and L2 solutions

> ML Prep screening item.

- Stable ID: `ml-screen-optimization-standard-l1-l2`
- Collection: screening
- Area: Machine Learning
- Topic: Optimization
- Origin: original
- Difficulty: medium
- Expected time: 8 minutes
- Skills: objective-functions, optimization-stationary-points, optimization-convexity, optimization-regularization
- Item JSON: https://mlprep.iwase.dev/item/ml-screen-optimization-standard-l1-l2.json

## Problem

Minimize

$$
J_1(w)=\frac{1}{2}(w-3)^2+|w|\qquad\text{and}\qquad J_2(w)=\frac{1}{2}(w-3)^2+\frac{1}{2}w^2.
$$

Find both minimizers and explain their shrinkage behavior.


## Answer policy

The human page contains a collapsed answer. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `ml-screen-optimization-standard-l1-l2`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.