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For a vector v =[v1v2]Tv=[v1v2]T, let p( v )=(1v1)2+100(v2v21)2p(v)=(1v1)2+100(v2v12)2. Calculate the gradient and Hessian of pp, and confirm or reject that pp is convex everywhere
For a vector v=[v1v2]Tv=[v1v2]T, let p(v)=(1v1)2+100(v2v21)2p(v)=(1v1)2+100(v2v12)2. Calculate the gradient and Hessian of pp, and confirm or reject that pp is convex everywhere in 2R2. If the function is not convex everywhere, please specify with a plot the region where convexity does not hold. What minimizing challenges arise for functions which are not convex?
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