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Positive semidefinite matrix approximation with a trace constraint

Kouhei Harada(harada***at***msi.co.jp)

Abstract: We propose an efficient algorithm to solve positive a semidefinite matrix approximation problem with a trace constraint. Without constraints, it is well known that positive semidefinite matrix approximation problem can be easily solved by one-time eigendecomposition of a symmetric matrix. In this paper, we confirmed that one-time eigendecomposition is also sufficient even if a trace constraint is included. Although an additional binary search is necessary, it is not computationally expensive.

Keywords: positive semidefinite matrix approximation, nearest matrix, trace constraint, projection onto a simplex, simplex constraint

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 08/08/2018
Entry Accepted: 08/08/2018
Entry Last Modified: 08/08/2018

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