[NOVA Math] Seminar of Operations Research

The Center of Mathematics and Applications (NOVA Math), promote the Seminar of Operations Research with the title: "Nearest Correlation Matrices via Halfspace Projections". Yunier Bello-Cruz (Department of Mathematical Sciences at Northern Illinois University (NIU), IL, USA) is the speaker.

Abstract: 

The nearest correlation matrix problem asks for the closest positive semidefinite matrix with unit diagonal to a given symmetric matrix G, measured in the Frobenius norm. We introduce HBAP (Halfspace Best-Approximation Projection), a projection-based algorithm that approximates the positive semidefinite cone by intersections of supporting halfspaces and computes iterates via projections onto these simpler sets.
At each iteration, HBAP constructs two halfspaces, a supporting halfspace for the positive semidefinite cone derived from the squared-distance function, and a localization halfspace that enforces monotone progress, and projects the anchor point onto their intersection with the unit-diagonal affine subspace. Every iterate satisfies the unit-diagonal constraint by construction. We prove that HBAP is well defined and that the full sequence converges to the nearest correlation matrix to G. The projection subproblem at each step admits a closed-form reduction to a 2X2 linear complementarity problem, yielding an explicit update formula. Alternatively, the same projection can be computed via Dykstra-type inner iterations, for which we derive a natural splitting with fully explicit projectors.

May 06  (Wednesday), 14h30,  Room 217D Departmental Building.