The bank

Question 1

What is the most general way to define an optimization proplem

Answer 1

min f(x)

s.t.

x in X

We have an objective function which we either want to minimize or maximize. Then we have a feasible region, which is the region where we are allowed to take a solution from.
The result is that we seek to find the point in X that gives us the smallest value for the objective function (or the largest).

Question 2

What is x?

Answer 2

a column vector. When we write it we typically say x=(x1, x2, …, xn)^T with the transpose to indicate this.
This also means that whenever we use a column vector and multiply by some matrix or other vector, we take the scalar product, we need to say x^Tb, to indicate that we’re talking about (x1, x2, .., xn)b

Question 3

Explain this notation:

z-star = f(x-star)

Answer 3

optimal objective function value z is given by the optimal decision variables through the objective function

Question 4

when do we have an integer programming problem?

Answer 4

When at least one of the variables are integer restricted

Question 5

Define a network problem

Answer 5

A network problem is one that can be described using arcs and nodes (a graph).