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Exam 8: Nonlinear Optimization Models

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

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Investment manager Max Gaines wishes to develop a mutual fund portfolio based on the Markowitz portfolio model.He 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 4%.Formulate the appropriate nonlinear program.​ ​

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IS = proportion of portfolio invested in...

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The interpretation of the dual price for nonlinear models is different than the interpretation of the dual price for linear models.

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

Any feasible solution to a blending problem without pooled components is feasible to the problem with pooled components.

A feasible solution is a global optimum if no other feasible solutions with a better objective function value are found in the immediate neighborhood.

A convex function is

When components share a storage facility,they are called

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.​

Financial planner Minnie Margin has a substantial number of clients who wish to own a mutual fund portfolio that matches,as a whole,the performance of the Russell 2000 index.Her task is to determine what proportion of the portfolio should be invested in each of the five mutual funds listed below so that the portfolio most closely mimics the performance of the Russell 2000 index.Formulate the appropriate nonlinear program.​ ​

The function f (X,Y)= X ² + Y ² has a single global minimum and is relatively easy to minimize.

Nonlinear programming algorithms are more complex than linear programming algorithms.

A feasible solution is a global optimum if no other feasible points with a better objective function value are found in the feasible region.

In the case of functions with multiple local optima,most nonlinear optimization software methods can get stuck and terminate at a local optimum.

When components (or ingredients)in a blending problem must be pooled,the number of feasible solutions is reduced.

The Markowitz mean-variance portfolio model presented in the text is a convex optimization problem.

For a typical nonlinear problem,if you change the right-hand side by even a small amount,the dual value changes.

Which of the following is NOT true regarding a concave function?

Investment manager Max Gaines has several clients who wish to own a mutual fund portfolio that matches,as a whole,the performance of the S&P 500 stock index.His task is to determine what proportion of the portfolio should be invested in each of the five mutual funds listed below so that the portfolio most closely mimics the performance of the S&P 500 index.Formulate the appropriate nonlinear program.​ ​

Any feasible solution to a blending problem with pooled components is feasible to the problem with no pooling.