Optimisation

Convex optimisation
Barrier method
Lagrange multipliers
The Necessity Theorem
Dual Problem
Complimentary Slackness
Economist perspective (not important)
Linear Program
Dual Problem in Linear Programs (most important lemma)
Optimality Condition in Linear Programming
Simplex method
Two-person Zero-sum Games
The Maximal Flow Problem
The Transportation Problem

Main objective

Minimize functions
subject to where

is objective function

"" is functional constraint
regional constraint

If s.t. for all
is called optimal
is the optimal cost

is called feasible set

If is not empty then the problem is feasible

is the same as where

, the coordinates of are called decision variables.