In disciplines such as robotics and aerospace engineering, there is an increasing demand to find control policies that maximize system performance specified in terms of decreasing effort, reducing fuel consumption, or generating graceful motions to achieve complex tasks. Such objectives can be expressed in terms of a scalar cost function that must be minimized subject to various physical constraints. Due to the importance of solving these problems, numerous algorithms have been proposed. A common approach employed in many of these algorithms is to discretize the continuous-time problem and obtain a finite-dimensional nonlinear programming problem that can be solved using a general-purpose nonlinear optimization solver. However, casting the problem in this manner destroys the inherent structure of the optimal control problem and results in large-scale problems that are computationally expensive to solve. To address these issues we propose an efficient sequential quadratic programming method that preserves the structure of the optimal control problem and exhibits favorable computational complexities with respect to the problem variables. This talk will focus on the class of Linear Quadratic optimal control problem with general path-state and control constraints. We demonstrate the computational gains and illustrate the properties of the algorithm with several numerical examples.