🎓 Deeper Dive — Adults

Optimisation finds the input that minimises (or maximises) an objective function, possibly with constraints.

Unconstrained: set ∇f(x*) = 0 and check Hessian. Constrained: use Lagrange multipliers — Lagrangian L = f(x) + Σ λᵢ gᵢ(x).

Gradient descent: xₙ₊₁ = xₙ − α·∇f(xₙ). Step in the direction of steepest decrease.

Linear programming (LP): linear objective + linear constraints — solved via simplex method. Convex optimisation guarantees global minimum.

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