Phase 10
Convex Optimization & Numerical Methods
Phase 10 of the Quant Academy curriculum.
10.1Full Lesson
Convex Sets and Convex Functions
The geometry that makes optimization tractable: no bad local minima.
10.2Full Lesson
Convex Optimization Problems and Optimality Conditions
Standard form, why local equals global, and the first-order optimality test.
10.3Full Lesson
Lagrangian Duality and the KKT Conditions
Turning constraints into prices, bounding the optimum, and certifying it.
10.4Full Lesson
Algorithms: Gradient Descent and Newton's Method
How we actually minimize: first-order steps, second-order steps, and why conditioning matters.
10.5Full Lesson
Applications: Portfolio Optimization and Regularization
Convex optimization at work: minimum-variance portfolios and ridge/lasso estimators.