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.