ABSTRACT
This chapter aims to set up a solution process for multivariable optimization problems, and recognize when applicable constraints are required. It introduces both constrained and unconstrained nonlinear optimization. For a more thorough coverage, the chapter suggests studying complete texts on the subject such as Ruszczynski’s Nonlinear Optimization. The definitions and theorems from the previous section are put to work to solve a set of unconstrained optimization problems in the following examples. Tides change the sea level around an island. Local tidal variation is influenced by a number of factors many of which are based on local topography. The chapter turns to an interesting and quite useful application of multivariate optimization: finding the least squares regression line fitting a data set. The Newton-Raphson iterative root finding technique using the partial derivatives of the function provides an alternative numerical search method for an optimum value when modified appropriately.
