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.