Phase 1: Calculus & Optimization · ~90 minutes · Python
Convex Optimization
Convex problems have one valley. Neural networks have millions. Knowing the difference matters.
Hiring signal: Understanding of convex optimization internals
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: Phase 1, Lessons 04 (Calculus for ML), 08 (Optimization) Time: ~90 minutes
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
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