One of the most challenging (“nasty” may be a better description) nonlinear least-squares problems (Jennrich and Sampson 1968) has yi = 2i + 2 and gi(θ1, θ2) = exp(iθ1) + exp(iθ2) for i = 1,...,n =...

One of the most challenging (“nasty” may be a better description) nonlinear least-squares problems (Jennrich and Sampson 1968) has yi = 2i + 2 and gi(θ1, θ2) = exp(iθ1) + exp(iθ2) for i = 1,...,n = 10. (a) Draw contour and surface plots of the sum-of-squares function S(θ1, θ2). (b) Try to solve this using nllsq (or any other optimizer) starting from (0.3, 0.4). (c) Is the sum-of-squares function S(θ1, θ2) locally quadratic around the optimum at (.2578, .2578)?