blockSQP is a sequential quadratic programming method for finding local solutions of nonlinear, nonconvex optimization problems. It is particularly suited for ---but not limited to---problems whose Hessian matrix has block-diagonal structure such as problems arising from direct multiple shooting parameterizations of optimal control or optimum experimental design problems. blockSQP has been developed around the quadratic programming solver qpOASES to solve the quadratic subproblems. Gradients of the objective and the constraint functions must be supplied by the user. Second derivatives are approximated by a combination of SR1 and BFGS updates. Global convergence is promoted by the filter line search of Waechter and Biegler that can also handle indefinite Hessian approximations.