Computational Approach to Function Minimization and Optimization with Constraints
This research conducted analyzes function minimization and optimization in the MATLAB programming environment. Different methods are examined and an assessment is made on which tool to utilize given an arbitrary function. This function can be of many types such as quadratic, linear, least squares, smooth nonlinear differential equation, or non-smooth differential equation. The constraints can be of many types as well such as bound, linear, general smooth, and discrete. It is important to note that optimization can also be done on functions which are not bound by constraints. Optimization methods are assessed under two categories, accuracy and computation time, in an attempt to determine the best optimizer to be used given a set type of function. In addition, this research focuses on the function minimization process of typical optimization testing functions. With system optimization becoming a growing field, this research has impactful implications on its computational approach and improving efficiencies of such processes.