An algorithm for continuous type optimal location problem

In this paper, we extend the ordinary discrete type facility location problems to continuous type ones. Unlike the discrete type facility location problem in which the objective function is not everywhere differentiable, the objective function in the continuous type facility location problem is strictly convex and continuously differentiable. An algorithm without line search for solving the continuous type facility location problems is proposed and its global convergence, linear convergence rate is proved. Numerical experiments illustrate that the algorithm suggested in this paper has smaller amount of computation and quicker convergence rate than the gradient method and conjugate direction method in some sense.