Sensitivity Analysis of Basins of Attraction for Gradient-Based Optimization Methods

This project is an analysis of the effectiveness of five distinct optimization methods in their ability in producing clear images of the basins of attraction, which is the set of initial points that approach the same minimum for a given function. Basin images are similar to contour plots, except that they depict the distinct regions of points--in unique colors--that approach the same minimum. Though distinct in goal, contour plots are useful to basin research in that idealized basin images can be inferred from the steepness levels and location of extrema they depict. Effectiveness of the method changes slightly depending on the function, but is generally defined as how closely the basin image models contour information on where the true minima are located, and by the clarity of the resulting image in depicting well-defined regions. The methods are tested on four distinct functions which were chosen to assess how each method performs in the presence of various challenges. This project ranks the five methods for their overall effectiveness and consistency across the four functions, and also analyzes the sensitivity of the methods when small changes are made to the function. In general, less sensitive and consistently effective methods are more applicable and reliable in applied optimization research.