Q: Discuss the differences between linear and nonlinear optimization methods. Include specific examples of nonlinear optimization methods and discuss which aspects of these models make them different from traditional linear optimization methods.

Student: Linear optimization is a common technique used to illustrate the relationship between decision variables with a clearly defined objective function with a straight line. Nonlinear optimization is utilized when the variables are nonlinear (e.g. root or squared). If we were to graph a nonlinear relationship, it would always be curved. I used water banking as an example in a previous post but another example could be risk management in a mutual fund portfolio. On one hand the portfolio manager wants to be able to report gains for the next quarter but they also want to be able to minimize risky behavior at the same time. These two objectives do not have a linear relationship.

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