# ✅ Checkpoint: constrained optimization and descent

By Better Wise

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## Contents

Part of [🧮 Mathematics for Machine Learning 2: Calculus and Optimization for Training Models](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training.md)

- **📐 First-order derivatives: gradients, Jacobians and the chain rule**
  - [📐 From partial derivatives to the gradient vector](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/partial-derivatives-to-gradient-vector.md)
  - [🧮 Jacobians of vector-valued functions](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/jacobian-vector-valued-functions.md) (sign-in required)
  - [🔗 Chain rule for composed functions](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/chain-rule-composed-functions.md)
  - [✅ Checkpoint: first-order derivatives](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/checkpoint-first-order-derivatives.md)
- **📉 Second-order behavior and convexity**
  - [🌀 Hessians and second-order behavior](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/hessians-second-order-behavior.md)
  - [📈 Taylor expansions, convexity and local minima](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/taylor-expansions-convexity-local-minima.md)
  - [✅ Checkpoint: curvature and convexity](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/checkpoint-curvature-and-convexity.md)
- **⛰️ Constrained optimization and gradient descent**
  - [⚖️ Lagrange multipliers for constrained problems](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/lagrange-multipliers-constrained-problems.md)
  - [🔽 Gradient descent and learning rate behavior](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/gradient-descent-learning-rate-behavior.md) (premium content)
  - [✅ Checkpoint: constrained optimization and descent](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/checkpoint-constrained-optimization-descent.md) (premium content) — this lesson
- [Course cheatsheet](https://everwise.study/courses/mathematics-for-machine-learning-2-calculus-and-optimization-for-training/cheatsheet.md) (premium content)