Quiz Chapter 09.01: Golden Section Search Method

1. Which of the following statements is incorrect regarding the Equal Interval Search and Golden Section Search methods?

Both methods require an initial boundary region to start the search

The number of iterations in both methods are affected by the size of

\varepsilon

Everything else being equal, the Golden Section Search method should find an optimal solution faster.

Everything else being equal, the Equal Interval Search method should find an optimal solution faster.

2. Which of the following parameters is not required to use the Golden Section Search method for optimization?

The lower bound for the search region

The upper bound for the search region

The golden ratio

The function to be optimized

3. When applying the Golden Section Search method to a function $f(x)$ to find its maximum, the $f(x_{1}) > f(x_{2})$ condition holds true for the intermediate points $x_{1}$ and $x_{2}$ . Which of the following statements is incorrect?

The new search region is determined by

\left[ x_{2}, \, x_{u} \right]

The intermediate point

x_{1}

stays as one of the intermediate points

The upper bound

x_{u}

stays the same

The new search region is determined by

\left[ x_{l}, \, x_{1} \right]

4. In the graph below, the lower and upper boundary of the search is given by $x_{1}$ and $x_{3}$ , respectively. If $x_{4}$ and $x_{2}$ are the initial intermediary points, which of the following statement is false?

The distance between

x_{2}

and

x_{1}

is equal to the distance between

x_{4}

and

x_{3}

The distance between

x_{4}

and

x_{2}

is approximately 0.618 times the distance between

x_{2}

and

x_{1}

The distance between

x_{4}

and

x_{1}

is approximately 0.618 times the distance between

x_{4}

and

x_{3}

The distance between

x_{4}

and

x_{1}

is equal to the distance between

x _{2}

and

x_{3}

5. Using the Golden Section Search method, find two numbers whose sum is $90$ and their product is as large as possible. Use the interval $\left[ 0, \, 90\right]$ .

30

and

60

45

and

45

38

and

52

20

and

70

6. Consider the problem of finding the minimum of the function shown below. Given the intermediate points in the drawing, what would be the search region in the next iteration?

\left[ x_{2}, \, x_{u} \right]

\left[ x_{1}, \, x_{u} \right]

\left[ x_{l}, \, x_{1} \right]

\left[ x_{l}, \, x_{2} \right]