TRANSFORMING ILL-CONDITIONED CONSTRAINED PROBLEMS USING PROJECTIONS

In this short note we consider the general problem of solving certain ill-conditioned constraint problems. We propose a strategy of transfor ming the original problem by projecting the constraint onto an auxilia ry surface (e.g. a hyperplane) in such a way that the transformed prob lem possesses a well-defined solution. The technique has been utilized to tackle two ill-conditioned problems-the Constrained Angle Bisector Problem and a Constrained Location Problem. The former problem, which has applications in image processing, involves bisecting an arbitrary angle subject to a simple quadratic constraint. The latter problem in volves a location assignment problem in which the locations are extern al to the boundary from which services are provided.