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 MULTIPLE CHOICE TEST GOLDEN SECTION SEARCH  METHOD OPTIMIZATION Pick the most appropriate answer.

Q1. 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

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.

Q2. 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

Q3. When applying the Golden Section Search method to a function f(x) to find its maximum, the  f(x1)>f(x2) condition holds true for the intermediate points x1 and x2. Which of the following statements is incorrect?

The new search region is determined by [x2, xu ]

The intermediate point x1 stays as one of the intermediate points
The upper bound xu stays the same
The new search region is determined by  [xl, x1 ]

Q4.  In the graph below, the lower and upper boundary of the search is given by x1 and x3  respectively. If  x4 and x2 are the initial intermediary points, which of the following statement is false?

The distance between x2 and x1 is equal to the distance between x4 andx3

The distance between x4 and x2 is approximately 0.618 times the distance between x2 and x1

The distance between  x4 and x1 is approximately 0.618 times the distance between x4 and x3

The distance between x4 and x1 is equal to the distance between x2 andx3

Q5.  Using the Golden Section Search method, find two numbers whose sum is 90 and their product is as large as possible. Use the interval [0,90].

30 and 60

45 and 45

38 and 52

20 and 70

Q6. 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?

[x2, xu ]

[x1, xu ]

[xl, x1 ]

[xl, x2 ]

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