Chapter 5 Non-Linear Programming (NLP)

In one general form, the nonlinear programming problem is to find \(\mathbf{x}=\left(x_{1}, x_{2}, \ldots, x_{n}\right)\) so as to maximize \(f(\mathbf{x})\) subject to \(g_{i}(\mathbf{x}) \leq b_{i} \text{, for } i=1,2, \ldots, m\) and \(\mathbf{x} \geq \mathbf{0}\) where \(f(\mathbf{x})\) and the \(g_{i}(\mathbf{x})\) are given of the \(n\) variables.

Nonlinear programming problems come in many different shapes and forms. Unlike the simplex method for linear programming, no single algorithm can solve all these different types of problems. Instead, algorithms have been developed for various individual classes (special types) of nonlinear programming problems. (Hillier 2012)

Non-linear programming can be divided usefully into convex programming and non-convex programming. (Williams 2013)

References

Hillier, Frederick S. 2012. Introduction to Operations Research. Tata McGraw-Hill Education.

Williams, H Paul. 2013. Model Building in Mathematical Programming. John Wiley & Sons.