## Multi-Variable Optimization:

Convex sets; geometric properties of functions: convex functions, their characterisations, properties and applications; further geometric properties of functions: quasi-convex functions, their characterisations, properties and applications; unconstrained optimisation: geometric characterisations, characterisations using calculus and applications; constrained optimisation with equality constraints: geometric characterisations, Lagrange characterisation using calculus and applications; properties of value function: envelope theorem and applications