Quadratic Interpolation Method in Optimization
Explore the efficiency of quadratic interpolation method in optimization, focusing on normalization, approximation, and refitting stages. Learn how to apply this method with an example and iterations.
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Technical Engineering College / Al-Najaf Al-Mustansiriyah University College of Engineering Technical College / Al-Najaf Communications Techniques Eng. Dpt. Communications Techniques Eng. Dpt. Electrical Engineering Department PhD courses /Comm. Eng./2018-2019 Computer Networks-4thClass-2011/2012 Computer Networks-4thClass-2015/2016 Main Topics Quadratic interpolation method
c Quadratic Interpolation Method This method is an interpolation method and in general interpolation methods are more efficient in optimization than elimination methods. This method depends the function values only; so it is useful to find the minimizing step ( ) of functions f (x). The minimum step ( ) in this method is obtained via the following three stages Stage1 Stage2 Stage3 Approximation Normalization Refitting
c Quadratic Interpolation Method Stage1: Normalization Recall that ? ? = ? ? + ?? ? Where = [?1?2?3 ??] ? = [?1?2?3 ??] Note: This stage is not required if the one-dimensional minimization
c Quadratic Interpolation Method Stage2: Approximation This can be done by the following two procedures: Procedure 21quadratic 2.pdf Procedure 2 2quadratic 3.pdf Stage3: Refitting This can be done by the following two procedure: Procedure 3quadratic 4.pdf
c Quadratic Interpolation Method Example: Solution: Stage1: pass Stage2: iteration21 quadratic 6.pdf iteration22quadratic 7.pdf Satge3: iteration3 quadratic 8.pdf
