Exam 13: Nonlinear Optimization Models

A(n) __________ is a set of points defining the minimum possible risk for a set of return values.

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

A ____________ is the shadow price of a binding simple lower or upper bound on the decision variable.

The reduced gradient is analogous to the ___________ for linear models.

A nonlinear function with term to the power of two is known as a

Excel Solver's __________ is based on a method that searches for an optimal solution by iteratively adjusting a population of candidate solutions.

Using the graph below, which of the following is true of the above function? ​

If the portfolio variance were equal to zero, the amount of risk would be

Jim must solve a nonlinear optimization problem where point A should be within a radius of 15 centimeters from each of the points B, C, D, E and F. The decision variables are defined as below. X = horizontal coordinate of point A Y = vertical coordinate of point A The data on the distances is given below: Horizontal Coordinate Vertical Coordinate B 9 11 C 14 18 D 18 22 E 13 16 F 17 21 Formulate and solve a model that minimizes the maximum distance from point A to each of the points B, C, D, E, and F. Round all your answers to three decimal places.

Consider the following data on the returns from bonds. nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; Year Bon d 1 0.20 0.126 0.321 -0.39 -0.67 0.135 0.52 0.75 Bon d 2 0.128 0.21 0.325 -0.243 0.169 0.125 0.304 0.286 Bon d 3 0.167 0.27 0.426 -0.84 0.143 -0.46 0.147 0.704 a. Construct the Markowitz portfolio model using a required expected return of at least 15 percent. Assume that the 8 scenarios are equally likely to occur. b. Solve the model using Excel Solver.

Solving nonlinear problems with local optimal solutions is performed using _____________, in Excel Solver, which is based on more classical optimization techniques.

In reviewing the image below, what is the minimum value for this function?

A function that is bowl-shaped down is called a ___________ function.

Develop a model that minimizes semivariance for the data given below with a required return of 15 percent. Define a variable $d _ { s }$ for each scenario and let $d _ { s } \geq \bar { R } - R _ { s }$ with $d _ { s }$ = 0. Then make the objective function: Min $1 / 4 \sum _ { s = 1 } ^ { 4 } d _ { s } ^ { 2 }$ . Scenario Mutual Fund Year 1 Year 2 Year 3 Year 4 Large-Cap Growth 41.54 36.18 32.76 -20.63 Large-Cap Value 32.45 44.78 28.61 38.49 Small-Cap Growth 26.13 7.04 -23.97 45.67 Small-Cap Value 37.56 18.53 27.53 -5.48 Solve the model you developed with a required expected return of at least 15 percent.

Consider the following data on the returns from bonds. Y ear Bon d 1 0.200 0.026 0.121 -0.139 -0.167 0.135 0.152 Bon d 2 0.128 0.100 0.125 -0.243 0.269 0.225 0.204 Bon d 3 0.067 0.700 0.226 -0.184 0.234 -0.146 0.047 Develop and solve the Markowitz portfolio model using a required expected return of at least 15 percent. Assume that the 8 scenarios are equally likely to occur. Use this model to construct an efficient frontier by varying the expected return from 2 to 18 percent in increment of 2 percent and solving for the variance. Round all your answers to three decimal places.