I'm having difficulties with the Nelder and Mead method and have no clue how to solve this question. Can someone please help out? Its urgent!! Been busy figuring it out for 3 days straight????
I had no idea what the "Nelder and Mead method" was until I looked it up on the internet.
What I would do to "Find the stationary points of the function f(x,y)=x2+3(y−1)4" is to set the "gradient" equal to 0. The gradient is gradf=∇f=∂x∂fi+∂y∂fj=2xi+12(y−1)3j. Setting that equal to 0 gives 2x= 0 and 12(y−1)3=0 so that x= 0 and y= 1. The only stationary point is (0, 1). The "Hessian" mentioned is the determinant ∣∣∣∣∣∣∂x2∂2f∂x∂y∂2f∂x∂y∂2f∂y2∂2f∣∣∣∣∣∣=(∂x2∂2f)(∂y2∂2f)edited−(∂x∂y∂2y)2=2(12)−0=24. Since that is positive the stationary point is a minimum.
Without being that technical, we could observe that x2 is a parabola opening upward while 3(y−1)4 also opens upward. Again that tells us that the stationary point is a minimum.
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