GLOBAL MINIMIZATION USING COUPLED LOCAL MINIMIZERS AND POTENTIAL APPLICATIONS IN GEOPHYSICAL DATA

Abstract

Mathematical optimization of a function is usually necessary in every field of science. Optimization is performed to find the ideal solution to a well-defined quantitative problem in a variety of disciplines. Fundamentally, an optimization problem involves maximizing or minimizing a cost/benefit function by systematically selecting input values from within a permitted set and calculating the function's value. In Geophysics, we employ optimization schemes to solve inverse problems, which are the backbone of any geophysical workflow, to calculate causal parameters from observational data. A lot of optimization methods, linear and stochastic/probabilistic, are popularly used today but each have their own set of problems. This dissertation addresses the latter and focuses on a relatively uncommon but efficient method applicable to global optimization of functions that may possess multiple local optima (minima/maxima), by using global approach, co-operative coupling and quick convergence. The method is then tested to ascertain the quality of its solution. Potential Geophysical applications are also discussed