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On a new class of matrix support functionals with applications

J.V. Burke(jvburke***at***uw.edu)
Tim Hoheisel(hoheisel***at***mathematik.unui-wuerzburg.de)

Abstract: A new class of matrix support functionals is presented which establish a connection between optimal value functions for quadratic optimization problems, the matrix-fractional function, the pseudo matrix-fractional function, and the nuclear norm. The support function is based on the graph of the product of a matrix with its transpose. Closed form expressions for the support functional and its subdifferential are derived. In particular, the support functional is shown to be continuously differentiable on the interior of its domain, and a formula for the derivative is given when it exists.

Keywords: Support function, quadratic programming, value function, matrix-fractional function, nuclear norm, subdifferential, normal cone

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Linear, Cone and Semidefinite Programming (Semi-definite Programming )


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Entry Submitted: 08/28/2014
Entry Accepted: 08/28/2014
Entry Last Modified: 08/28/2014

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