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Part of Standard Excel Installation Finds the root of a scalar function. GOALSEEK. Recall that root-finding methods (e.g., bisection method, Newton’s 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.

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goalseek

Part of Standard Excel Installation

Finds the root of a scalar function

GOALSEEK
  • Recall that root-finding methods (e.g., bisection method, Newton’s 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
goalseek example1

Make use of named ranges in Excel

    • Create solution variable cell “xval” and target cell “fofx”
GOALSEEK - Example
goalseek example2

Input the function into the “target cell”

    • Use the named variable
      • Type “=xval – cos(xval)” into the target cell
GOALSEEK - Example
goalseek example3

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
GOALSEEK - Example
goalseek1
GOALSEEK

Goal Seek found on Data Tab under “What-If Analysis”

solver

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

SOLVER
solver1

Uses a gradient-based method (like Newton’s 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)

SOLVER
finding the add ins in excel
FINDING The add-ins in Excel

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

finding the add ins in excel1
Finding The Add-ins in Excel

Make sure Solver Add-In is checked and click ok

finding the solver add in
Finding the SOLVER Add-in

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

solver example1

Use named ranges to establish variables for ‘xval’ and ‘yval’

Use named range to create a target cell ‘fxy’

SOLVER - Example
solver example2

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”)

SOLVER - Example
microsoft help on solver

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.
MicroSoft Help on “SOLVER”
example 2 invoking the solver function
Example 2: Invoking the SOLVER function

Solver is found on far right of Data tab

microsoft help on solver1

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.
MicroSoft Help on “SOLVER”
microsoft help on solver2

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.
  • Click Solve.
  • To keep the solution values on the worksheet, click Keep Solver Solution in the Solver Results dialog box.
MicroSoft Help on “SOLVER”
microsoft help on solver3

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.
MicroSoft Help on “SOLVER”
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