We consider the optimization of a cost functional defined for a fluid flowing through a channeL Parameters control the shape of an obstruction in the flow, and the strength of the inflow. The problem is discretized using finite elements. Optimization algorithms are considered which use either finite differences or sensitivities to estimate the gradient of the cost functional. Problems of scaling, local minimization, and cost functional regularization are considered. Methods of improving the efficiency of the algorithm are proposed. / Ph. D.