Advanced Design Technique (Multidisciplinary Optimization [Engineering])

PART A: Set up an objective function for your design project and identify the constraints involved. Prepare a presentation slide and a short write-up.

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PART B: Minimize f(x) = x sin x

Check what happens if x = 1.0769 at any point during the search.

1) Find the solution using Newton’s method.

Start from the initial bound points x0 = -0.5 & x=1.5

Decide when x* has converged, note the number of function iterations & function evaluations.

Count each calculation ff’ or f” as one function evaluation.

2) Find the solution using Golden Section method.

Start from initial bound points xL= -0.5 and xU = 1.5

Decide when x* has converged, note the number of function iterations & function evaluations.

Count each calculation ff’ or f” as one function evaluation.

3) Compare the number of iterations & function evaluations required by Newton’s method to the number required by the Golden Section.