We investigate numerical algorithms for viscoelastic fluid flows with defective boundary conditions, where only flow rates or mean pressures are prescribed on parts of the boundary. The defective boundary condition problem is formulated as a minimization problem, where we seek boundary conditions of the flow equations which yield an optimal functional value. Two different approaches are considered in developing computational algorithms for the constrained optimization problem, and results of numerical experiments are presented to compare performance of the algorithms. (C) 2011 Elsevier B.V. All rights reserved.