A simple algorithm for location in a closed convex domain

For building a power plant, a warehouse, an oil refining factory or a trade mall, it is important to choose a location in a closed convex domain. The original methods for Fermat location either are ineffective when a trial location is an extreme point or are very complex. For very general single location in a closed convex domain, a simple algorithm with global convergence is proposed. The algorithm belongs to the family of gradient methods, but it overcomes the drawback that the original gradient methods are ineffective when a trial location is an extreme point, and may not need a linear search. The convergence rate of the algorithm is faster than the rate of the original gradient methods.