Calibrating Least Squares Covariance Matrix Problems with Equality and Inequality Constraints

Yan Gao(yangaonus.edu.sg)
Defeng Sun(matsundfnus.edu.sg)

Abstract: In many applications in statistics, finance, and insurance/reinsurance, one seeks a solution of finding a covariance matrix satisfying a large number of given linear equality and inequality constraints in a way that it deviates the least from a given symmetric matrix. The difficulty in finding an efficient method for solving this problem is due to the presence of the inequality constraints. Our approach is to reformulate the problem as a system of semismooth equations via the dual approach. We then design an inexact smoothing Newton method to solve the resulted semismooth system. At each iteration, we use the BiCGStab iterative solver to obtain an approximate solution to the generated smoothing Newton linear system. Our numerical experiments confirm the high efficiency of the proposed method.

Keywords: covariance matrix, smoothing Newton method, quadratic convergence

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization

Citation: Report, Department of Mathematics, National University of Singapore, June 2008

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Entry Submitted: 06/27/2008
Entry Accepted: 06/27/2008
Entry Last Modified: 06/27/2008

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