Slide 1

Part of Standard Excel Installation Finds the root of a scalar function Recall that root-finding methods (e.g., bisection method, Newtons method) rely on a change in sign of the objective function Any f(x) function used in GOALSEEK should have a well defined sign change

Slide 2

Use Excels GOALSEEK feature to find the root of f(x) = x cos(x) between 0 and 1.

Slide 3

Make use of named ranges in Excel Create solution variable cell xval and target cell fofx

Slide 4

Highlight cells that will be named. Under Formulas Tab select Create from Selection

Slide 5

Input the function into the target cell Use the named variable Type =xval cos(xval) into the target cell

Slide 6

Slide 7

Put an initial guess in the variable cell 0.5 is the middle of the interval, so use it Now invoke the GOALSEEK function You can use the named ranges in the GOALSEEK dialog box, or point and click

Slide 8

Goal Seek found on Data Tab under What-If Analysis

Slide 9

Slide 10

Then click OK

Slide 11

Slide 12

Solver is an add-in to Excel It is not installed by default SOLVER will find a particular value, the maximum, or the minimum of a scalar function of a vector

Slide 13

Uses a gradient-based method (like Newtons method) to find the root or the max/min Works very well for functions that have a well-defined minimum (or maximum), like a quadratic form (a parabola)

Slide 14

Go to Excel Options

Slide 15

Go to Add-Ins Tab on left and click Go at bottom

Slide 16

Make sure Solver Add-In is checked and click ok

Slide 17

Now go to Data tab and click on Solver on the far right

Slide 18

Find the minimum of f(x,y)=(x-5) 2 + (y-5) 2

Slide 19

Use named ranges to establish variables for xval and yval Use named range to create a target cell fxy

Slide 20

Slide 21

Put initial guesses for xval, yval in their cells (use (0,0)) Type the formula into the target cell (=(xval-5)^2 + (yval- 5)^2)

Slide 22

Slide 23

Invoke the SOLVER function

Slide 24

Define and solve a problem by using Solver On the Data Tab, click Solver (far right). If the Solver command is not on the Data Tab, you need to install the Solver add-in. In the Set Target Cell box, enter a cell reference or name for the target cell. The target cell must contain a formula.

Slide 25

Solver is found on far right of Data tab

Slide 26

To have the value of the target cell be as large as possible, click Max. To have the value of the target cell be as small as possible, click Min. To have the target cell be a certain value, click Value of, and then type the value in the box. In the By Changing Cells box, enter a name or reference for each adjustable cell, separating nonadjacent references with commas. The adjustable cells must be related directly or indirectly to the target cell. You can specify up to 200 adjustable cells.

Slide 27

Slide 28

To have Solver automatically propose the adjustable cells based on the target cell, click Guess. In the Subject to the Constraints box, enter any constraints you want to apply. constraints Click Solve. To keep the solution values on the worksheet, click Keep Solver Solution in the Solver Results dialog box.

Slide 29

Slide 30

To restore the original data, click Restore Original Values. Tips You can interrupt the solution process by pressing ESC. Microsoft Excel recalculates the worksheet with the last values found for the adjustable cells.