| This thesis introduces a globalization strategy for approximating global minima of zero-residual least-squares problems. This class of nonlinear programming problems arises often in data-fitting applications in the fields of engineering and applied science. Such minimization problems are formulated as a sum of squares of the errors between the calculated and observed values. In a zero-residual problem at a global solution, the calculated values from the model matches exactly the known data.; The presence of multiple local minima is the main difficulty. Algorithms tend to get trapped at local solutions when applied to these problems. The proposed algorithm is a combination of a simple random sampling, a Levenberg-Marquardt-type method, a scaling technique, and a unit steplength. The key component of the algorithm is that a unit steplength is used. An interesting consequence is that this approach is not attracted to non-degenerate saddle points or to large-residual local minima. Numerical experiments are conducted on a set of zero-residual problems, and the numerical results show that the new multi-start strategy is relatively more effective and robust than some other global optimization algorithms. |
