Optimization
Convexity, Lagrange multipliers, duality and dynamic programming.
16 planned
No page in this subject is open yet. The planned list below shows what is coming, in learning order.
Planned
In learning order. These are not pages yet.
- Dynamic programming: solving backward from the endAdvanced undergrad
- Convex sets and convex functionsAdvanced undergrad
- Why convex problems have no bad local minimaAdvanced undergrad
- Separating hyperplanes: a line between two convex setsAdvanced undergrad
- Lagrange multipliers: why the gradients line upIntro
- Linear programming: why the optimum sits at a cornerAdvanced undergrad
- Critical points in two variables: bowl, peak, or saddleIntro
- Farkas' lemma: either a solution or a certificateGraduate
- What a Lagrange multiplier is worth: shadow pricesAdvanced undergrad
- Inequality constraints and the KKT conditionsAdvanced undergrad
- Gradient descent and the step sizeAdvanced undergrad
- Two-stage stochastic programming: deciding before uncertainty resolvesGraduate
- Duality: the lower bound that meets the optimumGraduate
- Fitting a model by nonlinear least squaresAdvanced undergrad
- Quadratic programming: minimizing a bowl over a polygonAdvanced undergrad
- The Hamilton-Jacobi-Bellman equation: dynamic programming in continuous timeGraduate
How it connects
Builds on Linear algebra Calculus Regression Stochastic calculus and SDEs Probability
Leads to Arbitrage and risk-neutral pricing Equities and portfolios Market risk Numerical methods Regression Derivatives Hedging and calibration Volatility and jump models
Subjects marked “connection” are linked by a related idea, not by a prerequisite.