## Optimization on a 4th Order Polynomial Where Multiple Maxima Exist

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# Description

This model is a simple example demonstrating how GoldSim optimization works on a function that contains more than one local maximum or minimum value. The function used for this example is a quartic (4th order polynomial). The equation for this quartic equation is: y = ax^4 + bx^3 + cx^2 - dx + e

To run the optimization, go to the Run menu and click on Optimization. The objective function is to maximize the value of y by adjusting x. Enter the name "y" in the objective function and add x as the optimization variable. The parameters a thru e are constants. Note there are two possible maximum solutions in this function. The global maximum solution for this problem is y = 5892 where x is -83. A lessor maximum is located at x = 88 such that y = 5239.

# Additional Information

## Keywords

optimization, polynomial, math, minimum, optimum, maximum, best, search, maxima, local, optimal, global

## Categories

GoldSim Features & Capabilities, Optimization and Sensitivity Analysis