Concept clusters
Related ideas that live chapters apart, pulled onto one page — every factoring technique, every way to solve a quadratic, and more.
Every unconstrained-optimization method, and which one to pick
Gradient descent, Newton, quasi-Newton, conjugate gradient, derivative-free search, and stochastic/population methods — one decision chain spanning three chapters.
23 concepts →
How do you know a point is actually optimal?
FONC/SONC for unconstrained problems, KKT for constrained ones, and LP duality's certificate — every way this course proves a candidate solution really is the best one.
20 concepts →
Which way of handling inequality constraints do I use?
KKT says what an optimal point must satisfy once inequality constraints are in play; penalty, augmented Lagrangian, barrier, interior-point, and SQP are the algorithms that actually chase one down.
14 concepts →
Every way to establish convexity (and why it's worth checking)
The definition, the first-order tangent test, the second-order Hessian test, and the operations that build complex convex functions from simple ones — because convexity is what turns "a minimum" into "the minimum."
14 concepts →
Shadow prices and sensitivity — the same idea, twice
A Lagrange multiplier's marginal value and a linear program's dual variable are the same concept — met first in Chapter 6, formalized again in Chapter 8.
8 concepts →