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(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 [x_{2, }x_{u} ]
The
intermediate point
x_{1} stays as one of the intermediate
points Q4. 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} andx_{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} andx_{3} 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?
[x_{2, }x_{u} ] [x_{1, }x_{u} ] [x_{l, }x_{1} ] [x_{l, }x_{2} ]

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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 336205350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624, 0836981, 0836916, 0836805, 1322586. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Other sponsors include Maple, MathCAD, USF, FAMU and MSOE. Based on a work at http://mathforcollege.com/nm. Holistic Numerical Methods licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. 
