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Title: A Study on NonSymmetric Matrix-Valued Functions
Authors: YANG ZHE
Keywords: nonsymmetric matrix-valued function, smoothing function, definition, differential properties, semismoothness, generalized Jacobian
Issue Date: 18-Aug-2009
Citation: YANG ZHE (2009-08-18). A Study on NonSymmetric Matrix-Valued Functions. ScholarBank@NUS Repository.
Abstract: The nonsymmetric matrix-valued function plays an important role in some basic issues on designing and analyzing semismoothing/ smoothing Newton methods for nonsymmetric matrix optimization problems. We study some key properties of nonsymmetric matrix-valued functions and their smoothing counterparts. First we show that the nonsymmetric matrix-valued function is well defined and it inherit the continuity, differentiability, continuous differentiability, locally Lipschitz continuity, directional differentiability and (strongly) semismoothness from its corresponding real-valued function. Importantly, we give the formulas of the directional derivative and the generalized Jacobian of the nonsymmetric matrix-valued function. Next we introduce a generalized smoothing function for the nonsymmetric matrix-valued function and study the continuity, differential properties and semismoothness of it.
Appears in Collections:Master's Theses (Open)

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