Introduction to optimisation

The optimisation problem (inc min or max, equivalence between the two)

Local optima (definition, broad)

Optimising convex functions

Constrained optimisation

Unconstrained optimisation of differentiable functions

Stationary points and first-order conditions

Local minima, maxima and inflection points

Optimising convex and non-convex differentiable functions

Optimising functions of more than one variable

Hessian matrix

Linear optimisation

Linear optimisation with equality constraints

Multiple equality constraints (merge with above, and non-linear)

Linear optimisation with inequality constraints

The primal and dual problems of linear optimisation

Complementary slackness for linear optimisation

Farkas' lemma

Quadratic optimisation

The quadratic optimisation problem

Constrainted non-linear optimisation

The non-linear optimisation problem

Lagrange multipliers

The dual problem for non-linear optimisation

The weak duality theorem

Constrained convex optimisation

Slater's condition

The strong duality theorem

The Karush-Kuhn-Tucker conditions