Title: A New Approach for Solving The Trust-Region
                Subproblem in Nonlinear Programming


			    Ken Chan
		   The Aerospace Corporation
		 15049 Conference Center Drive
		       Chantilly, VA 20151
		     kenneth.f.chan@aero.org
		       http://www.aero.org


ABSTRACT

	This presentation deals with a new formulation of the solution of 
minimizing a quadratic objective function in n-dimensions over an 
n-dimensional ellipsoidal region. This problem is at the heart of nonlinear 
programming, known as the Trust-Region Subproblem (TRS). Existing algorithms 
are very complicated in structure, iterative in nature, time-consuming 
computationally and also require substantial computer memory. A closed form 
solution has been obtained for the TRS, meaning that there are no iterations, 
convergence of the sequence is not an issue, and the approach does not require
the dichotomy into interior and exterior point methods. Only a polynomial 
equation need be solved. The formulation is based on the conditions for 
tangency of two surfaces described by quadratic forms. The characteristic 
equation for eigenvalues and its associated derivative equation are expressed 
in fundamental forms which yield winged-diagonal determinants in simple forms.
Efficient algorithms have been constructed to obtain the minimization of the 
objective function even for the case of large n.