Deck 8: Nonlinear Optimization Models

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

Nonlinear optimization problems can have only one local optimal solution.

Answer 3

False

Question 4

Nonlinear programming algorithms are more complex than linear programming algorithms.

Question 5

In the Bass model for forecasting the adoption of a new product, the objective function

A)minimizes the sum of forecast errors.
B)minimizes the sum of squared forecast errors.
C)maximizes the number of adoptions.
D)maximizes the number of adoptions and imitations.

Question 6

Components that share a storage facility are called

A)constrained components.
B)indexed components.
C)blended components.
D)pooled components.

Question 7

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

Question 8

An investor can pick the mean-variance tradeoff that he or she is most comfortable with by looking at a graph of the

A)feasible region.
B)pooled components.
C)rolling horizon.
D)efficient frontier.

Question 9

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

Question 10

The key idea behind constructing an index fund is to choose a portfolio of securities that

A)is a mix of growth-oriented and income-oriented stocks.
B)minimizes risk without sacrificing liquidity.
C)mimics the performance of a broad market index.
D)balances short-term and long-term investments.

Question 11

The measure of risk most often associated with the Markowitz portfolio model is the

A)portfolio average return.
B)portfolio minimum return.
C)portfolio variance.
D)portfolio standard deviation.

Question 12

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

A)the coefficient of innovation
B)the coefficient of interaction
C)the coefficient of imitation
D)the estimated number of people to eventually adopt the new product

Question 13

If the coefficient of each squared term in a quadratic function is positive, the function is

A)concave.
B)convex.
C)elliptical.
D)sinusoidal.

Question 14

When the number of blending components exceeds the number of storage facilities, the number of feasible solutions to the blending problem

A)is reduced.
B)is increased.
C)is unchanged.
D)is zero.

Question 15

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

A)It is bowl-shaped down.
B)It is relatively easy to maximize.
C)It has multiple local maxima.
D)It has a single global maximum.

Question 16

A function is quadratic if its nonlinear terms have a power of 4.

Question 17

Many linear programming algorithms such as the simplex method optimize by examining only the extreme points of the feasible region.

Question 18

Which of the following is incorrect?

A)A global optimum is a local optimum in a nonlinear optimization problem.
B)A local maximum is a global maximum in a concave nonlinear optimization problem.
C)A global minimum is a local minimum in a convex nonlinear optimization problem.
D)A local optimum is a global optimum in a nonlinear optimization problem.

Question 19

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

Question 20

A convex function is

A)bowl-shaped up.
B)bowl-shaped down.
C)elliptical in shape.
D)sinusoidal in shape.

Question 21

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

Question 22

For a minimization problem, a point is a global minimum if there are no other feasible points with a smaller objective function value.

Question 23

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

Question 24

Each point on the efficient frontier is the maximum possible risk, measured by portfolio variance, for the given return.

Question 25

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

Question 26

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

Question 27

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

Question 28

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

Question 29

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

Question 30

The problem of maximizing a concave quadratic function over a linear constraint set is relatively difficult to solve.

Question 31

Because most nonlinear optimization codes will terminate with a local optimum, the solution returned by the codes will be the best solution.

Question 32

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

Question 33

There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution.