intro

Question 1

general optimisation problem:

Answer 1

minimise f(x) subject to x in Ω, Ω a subset of R^n

Question 2

x*:

Answer 2

a vector satisfying the constraints, aka an optimum/solution/minimiser

Question 3

convex set:

Answer 3

a set is convex if for all x,y in C (C subset of R^n) and λ in [0,1], λx+(1-λ)y in C, so for any two points the line segment connecting them is also in C

Question 4

convex function:

Answer 4

a function f:C->R^n is convex if C is convex and for all x,y in C and λ in [0,1], f(λx+(1-λ)y) <= λf(x)+(1-λ)f(y)