Decomposition Approach to Parametric Nonconvex Regression; Nuclear Resonance Analysis

Parameterized nonconvex regression is a difficult problem for any optimization solver packages, often resulting in approximations and linearizations of the problem in order to be able to arrive a solution, if the problem is even solvable at all. These changes to the initial problem are largely dependent upon having appropriate domain knowledge and still often times result in a sizable gap between the achieved solution and the best true solution. We propose a novel method of decomposing the global problem into small, overlapping windows. Thus, the independent windows are now solvable. Subsequently, we offer a novel, sequential method of parameter cardinality and parameter value agreement in order to stitch the windows back together to arrive at the solution to the initial global problem. While this method is problem agnostic, we demonstrate the successful results of its application to the nuclear data analysis problem of properly characterizing the resonances of the capture cross section for Copper-63. By being able to solve the 100 resonance problem, this method demonstrates it can solve up to the thousands of possible resonances an isotope can have within a single spin group.

Final draft, paperwork submitted by Dr. Ostrowski earlier today.