The film height distribution which yields the maximum load carrying capacity for the rectangular slider is determined using a PDE-constrained optimization solver. The gradient of the objective function, i.e. the load, with respect to the design variable, i.e. the film height distribution, is calculated using a discrete adjoint approach. It is shown that, in contrast to the linear slider, the load carrying capacity per unit length and at constant width of the optimized slider steadily increases with increasing length over width ratio.