The research objective of this award is to develop and implement first-order trust-search methods for use in large-scale data-generated optimization problems. Data-generated problems arise in applications such as signal and image processing. These problems are especially difficult to solve since the data are often high dimensional and are noisy, incomplete, and/or inexact. This research will develop first-order quasi-Newton trust-search methods for solving large data-generated problems. The methods to be used are trust-search methods, which are hybridizations of the most fundamental types of methods for unconstrained optimization: trust-region methods and line-search methods. Trust-search methods seek to implement line-search strategies in combination with trust-region theoretics to obtain more robust methods.
If successful, the results of this research will help scientists and engineers solve optimization problems involving large volumes of corrupted data. In today's world, scientific data are more abundant than ever before; moreover, projects are already underway to produce even more data at a faster rate. To keep pace, the emerging field of "big data" requires sophisticated, fast, robust, and large-scale numerical algorithms. This research will use linear algebra and optimization theory to develop software for processing and analyzing very large data sets. In particular, the results of this research will help solve important problems in image processing applications such as medical imaging, low-light video surveillance, and nocturnal ecological activity monitoring, where the generated data are not only very large but are very noisy. The algorithms will be disseminated publically for use within and outside the scientific community. Graduate students will be trained in scientific research and programming through this research, and the participation of students from under-represented backgrounds will be highly encouraged.
