Topic 1 Basics of Optimisation

Question 1

Define independent variable.

Answer 1

• Variable which can be freely set within the scope of the problem.
• Also called decision variable.
• Causes a change in the dependent variable(s)

Question 2

Define dependent variable

Answer 2

Variable which changes based on the independent variables.

Question 3

Define objective function

Answer 3

• Function of the independent variable(s) which produces a dependent variable.
• Also called the cost function

Question 4

Define optimisation

Answer 4

Process of selecting the best possible decision variable (or set of decision vector) from a range of possibilities which maximises or minimises (as required by the problem) the objective function response (decision variable value(s))

Question 5

What are the inputs to the objective function known as?

Answer 5

Independent variables

Question 6

What is the output of an objective function known as?

Answer 6

Dependent variable

Question 7

Define univariate function

Answer 7

• An objective function which has exactly one input value, i.e. the independen/decision variable has exactly one dimension

Question 8

What is the feasible space?

Answer 8

A subset of the set of all possble values of the decision variable, X [proper subset of] Omega.

Question 9

What is the difference between a global minimum point and a local minimum point?

Answer 9

A local minimum point is the minimum value within a specific region.
A global minimum point is the minimum value within the entire feasible space, X.

Question 9

What is the difference between a global minimum point and a local minimum point?

Answer 9

A local minimum point is the minimum value within a specific region.
A global minimum point is the minimum value within the entire feasible space, X.

Question 10

What is a weak local minimum point?

Answer 10

• A minimum point within a specified range which is one of a range of adjacent points, all with the same function response.
• It appears on a 2D graph as a point within a flat section of the objective function line.

Question 11

What is an inflection point?

Answer 11

Point at which the function changes from being increasing to decreasing or vice versa (i.e., the concavity changes)

Question 12

What is a discrete independent/decision variable?

Answer 12

A variable whose value counts a set of finite items.

Question 13

What is a continuous independent/decision variable?

Answer 13

• A variable whose value can take any value within a range

- E.g. A person’s height

Question 14

What is a binary independent/decision variable?

Answer 14

• A variable whose value takes one of two possible values

- E.g. heads or tails

Question 15

What is a nominal independent/decision variable?

Answer 15

Variable whose value represents a category which has no ordering.
- e.g. a person’s nationality

Question 16

What is an ordinal independent/decision variable?

Answer 16

• A variable whose value is from an ordered ranking
• May be discrete or continuous
• e.g. rating scale in a survey

Question 17

Define multivariate function

Answer 17

• Function which has multiple input values
• It may take a decision vector as input which contains multiple values
• e.g. f(x) = x_1 ^ 2 + x_2 ^ 2