Wu, Zili2024-08-152024-08-1519971997https://hdl.handle.net/1828/20208To deal with nonsmooth phenomena in mathematics and optimization, various kinds of subdifferentials have been introduced in the literature over the last two decades. Among them are the Clarke generalized gradient, the limiting subgradient, and the proximal subgradient. In this thesis, we provide some conditions that guarantee the nonemptiness of the proximal subgradient, and the sum rule for proximal subgradients to hold. We have also found a class of functions f that can be recovered up to a constant by the proximal subgradient of J or - J. Finally we provide some sufficient conditions for the existence of error bounds in terms of the above three subdifferentials.94 pagesAvailable to the World Wide WebThesis