ORTHOMAX rotation problem. a differential equation approach

In the present paper the ORTHOMAX rotation problem is reconsidered. It is shown that its solution can be presented as a steepest ascent flow on the manifold of orthogonal matrices. A matrix formulation of the ORTHOMAX problem is given as an initial value problem for matrix differential equation of first order. The solution can be found by any available ODE numerical integrator. Thus the paper proposes a convergent method for direct matrix solution of the ORTHOMAX problem. The well-known first order necessary condition for the VARIMAX maximizer is reestablished for the ORTHOMAX case without using Lagrange multipliers. Additionally new second order optimality conditions are derived and as a consequence an explicit second order necessary condition for further classification of the ORTHOMAX maximizer is obtained