Algorithms for Minimum Trace Factor Analysis

Abstract

Minimum trace factor analysis is a commonly used technique for providing the greatest lower bound to reliability, and a modification of the basic problem involves the maximization of this greatest lower bound with respect to suitably chosen weights. The underlying mathematical problems can be expressed as optimization problems with eigenvalue constraints, and it is well known that these can be nondifferentiable in the presence of multiple eigenvalues. In this paper, some recent developments in methods for working with constraints of this kind are exploited to provide methods which are second-order independent of the eigenvalue multiplicities. The effectiveness of the algorithms is demonstrated on some test problems. Minimum trace factor analysis is a commonly used technique for providing the greatest lower bound to reliability, and a modification of the basic problem involves the maximization of this greatest lower bound with respect to suitably chosen weights. The underlying mathematical problems can be expressed as optimization problems with eigenvalue constraints, and it is well known that these can be nondifferentiable in the presence of multiple eigenvalues. In this paper, some recent developments in methods for working with constraints of this kind are exploited to provide methods which are second-order independent of the eigenvalue multiplicities. The effectiveness of the algorithms is demonstrated on some test problems.