Combining algorithm for a kind of constrained location model

For very general single location on a closed convex domain, we propose a combining algorithm which has global convergence. The algorithm uses the trust region (TR) technique first, but it takes the gradient method which doesn't use a linear search instead of resolving the subproblem when the trial step is not successful. The algorithm overcomes the drawback that the original gradient methods are ineffective when an iterative point is an extreme point, and may not usually make a linear search. The algorithm has good quality as TR algorithm, but it avoids the linear cycle which may arise in TR algorithm.