A global optimization technique for zero-residual nonlinear least-squares problems
Velazquez Martinez, Leticia
Tapia, Richard A.
Doctor of Philosophy
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.