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Consider the Freudenstein and Roth test function f(x)= f;(x)² + f2(x)², xER?, where fi(x) =-13+x1 +((5– x,)x,– 2)x2, f2(x) =-29+x1 +((x2+1)x,– 14)x2. (i) Show that the function f has three stationary points. Find them and prove that one is a global minimizer, one is a strict local minimum and the third is a saddle point.

Consider the Freudenstein and Roth test function f(x)= f;(x)² + f2(x)², xER?, where fi(x) =-13+x1 +((5– x,)x,– 2)x2, f2(x) =-29+x1 +((x2+1)x,– 14)x2. (i) Show that the function f has three stationary points. Find them and prove that one is a global minimizer, one is a strict local minimum and the third is a saddle point.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Full steps please. I will rate soon. It is the Exercise 5.2 (i) in chapter 5 in the book Amri Beck, Introduction to nonlinear optimization.

Consider the Freudenstein and Roth test function f(x)= f;(x)² + f2(x)², xER?, where fi(x) =-13+x1 +((5– x,)x,– 2)x2, f2(x) =-29+x1 +((x2+1)x,– 14)x2. (i) Show that the function f has three stationary points. Find them and prove that one is a global minimizer, one is a strict local minimum and the third is a saddle point.
Transcribed Image Text:Consider the Freudenstein and Roth test function f(x)= f;(x)² + f2(x)², xER?, where fi(x) =-13+x1 +((5– x,)x,– 2)x2, f2(x) =-29+x1 +((x2+1)x,– 14)x2. (i) Show that the function f has three stationary points. Find them and prove that one is a global minimizer, one is a strict local minimum and the third is a saddle point.
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