Specific Subject: Design optimization

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Specific Subject: Design optimization
Example Problem for PhD subject qualifying exams The generalized logistic curve (a.k.a. Richard's curve) along with the S.L.R. (Susceptible Infectious and Removed) model are among the simplest models used in growth modeling and mathematical modeling of infectious diseases like the recent Coronavirus disease (COVID-19); see e.g., Figure 1 below. Coronavirus epidemic in Spain (SIR model) R * 1.745 3= 0.519 = 0.297 N = 239615 C 170328 5 Son 69287 RMSE 710 200 150 Prediction Actual Infected (x1000 cases) 100 50 03/01/20 04/01/20 05/01/20 0601/20 Date Infection Rate in Spain Total Infected: 126 168. Total Dead: 11947 10000 Actual Prediction 8000 6000 casesday 4000 2000 0 03/01/20 04/01/20 05/01/20 06/01/20 Date The generalized logistic function/curve is defined as: Y(t) = A +- K-A (C+Qe-B(-)) where Y is the prediction/projection at timet (commonly in days), A, K are the lower and upper asymptotes, respectively, Bis the growth rate, affects the value at t=0, vaffects the maximum growth position and M corresponds to the maximum growth time, if Q=v=1. Assuming now that C-Q-1 Question 1: formulate an optimization problem that determines the generalized logistic curve for a given set of country- specific timeseries data; use a simple least squares approach Question 2. Did you formulate the above problem as an unbounded or a constrained optimization problem; justify your selection in any case, and mention the type of constraints, if any, you are including in your formulation. Question 3: What is the cardinality of the design space? Question 4: Will you use A as a design variable or not? If yes, explain why and if not, specify the value you are going to use for A Question 5: Will you use K as a design variable or not? If yes, explain why and if not, specify the value you are going to use Question 6: Ista component of the design vector? Justify your answer in any case. for K.