Phase 1: Calculus & Optimization · ~90 minutes · Python

Convex Optimization

Convex problems have one valley. Neural networks have millions. Knowing the difference matters.

What you will learn

Test whether a function is convex using the definition, second derivative, and Hessian criteria
Implement Newton's method and compare its quadratic convergence against gradient descent
Solve constrained optimization problems using Lagrange multipliers and interpret KKT conditions
Explain why neural network loss landscapes are non-convex yet SGD still finds good solutions

Introduction

Type: Build
Language: Python
Prerequisites: Optimization
Time: ~90 minutes

Objective

Learning objectives

Test whether a function is convex using the definition, second derivative, and Hessian criteria
Implement Newton's method and compare its quadratic convergence against gradient descent
Solve constrained optimization problems using Lagrange multipliers and interpret KKT conditions
Explain why neural network loss landscapes are non-convex yet SGD still finds good solutions

Unlock the full lesson

You've read the first 2 sections. The rest of this lesson covers The Problem, The Concept, Build, Check Yourself, Key Terms & Next — plus a hands-on lab, quiz, and project artifact.

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Key terms in this lesson

Gradient Descent