A novel and efficient iterative optimization method has been developed for computing the maximum force observed as a cylinder is withdrawn from an annular interface between two fluids. This method can be used to find the interfacial tension from the experimental value of the maximum force and several other parameters related to the experiment. It also produces the interface shape, which can be highly curved when the vessel diameter is large relative to the cylinder diameter. The method, based on successive quadratic programming and the use of Lagrange multipliers to handle equality constraints, is not specific to the surface tension problem, but can be applied in the general case in which a function is to be minimized and the minimum value is equality constrained.