Nonsmooth Matrix Valued Functions Defined by Singular Values

Defeng Sun (matsundfnus.edu.sg)
Jie Sun (jsunnus.edu.sg)

Abstract: A class of matrix valued functions defined by singular values of nonsymmetric matrices is shown to have many properties analogous to matrix valued functions defined by eigenvalues of symmetric matrices. In particular, the (smoothed) matrix valued Fischer-Burmeister function is proved to be strongly semismooth everywhere. This result is also used to show the strong semismoothness of the (smoothed) vector valued Fischer-Burmeister function associated with the second order cone. The strong semismoothness of singular values of a nonsymmetric matrix is discussed and used to analyze the quadratic convergence of Newton's method for solving the inverse singular value problem.

Keywords: Fischer-Burmeister function, SVD, strong semismoothness, inverse singular value problem

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Complementarity and Variational Inequalities

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Technical Report, Department of Decision Sciences, National University of Singapore, December, 2002

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Entry Submitted: 01/21/2003
Entry Accepted: 01/21/2003
Entry Last Modified: 01/21/2003

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