Exam 8: Nonlinear Optimization Models

Functions that are convex have a single local maximum that is also the global maximum.

A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.

The value of the coefficient of imitation, q, in the Bass model for forecasting adoption of a new product cannot be negative.

Discuss the essence of the pooling problem in terms of the circumstances, objective, and constraints.

Which of the following is not a parameter of the Bass model for forecasting adoption of a new product?

Nonlinear optimization problems can have only one local optimal solution.

For a typical nonlinear problem, duals price are relatively insensitive to small changes in right-hand side values.

Financial planner Minnie Margin wishes to develop a mutual fund portfolio based on the Markowitz portfolio model. She needs to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the variance of the portfolio is minimized subject to the constraint that the expected return of the portfolio be at least 5%. Formulate the appropriate nonlinear program. $\text { Annual Returns (Flanning Scenarios) }$ Mutual Fund Year 1 Year 2 Year 3 Year 4 International Stock 22.37 26.73 4.86 2.17 Large-Cap Value 15.48 19.64 11.50 -5.25 Mid-Cap Value 17.42 20.07 -4.97 -1.69 Small-Cap Growth 23.18 12.36 3.25 3.81 Short-Term Bond 9.26 8.81 6.15 4.04