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Dykstra's Algorithm for a Constrained Least-squares Matrix Problem

✍ Scribed by René Escalante; Marcos Raydan

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
577 KB
Volume
3
Category
Article
ISSN
1070-5325

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✦ Synopsis

We apply Dykstra's alternating projection algorithm to the constrained least-squares matrix problem that arises naturally in statistics and mathematical economics. In particular, we are concerned with the problem of finding the closest symmetric positive definite bounded and patterned matrix, in the Frobenius norm, to a given matrix. In this work, we state the problem as the minimization of a convex function over the intersection of a finite collection of closed and convex sets in the vector space of square matrices.

We present iterative schemes that exploit the geometry of the problem, and for which we establish convergence to the unique solution. Finally, we present preliminary numerical results to illustrate the performance of the proposed iterative methods.

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