The method of Yeoet alto choose initial multipliers optimally for the quasi-linearization solution of optimal control problems with control bounds is extended to a wider class of optimal control problems with constraints. The constraints are inequality constraints on functions of the state and control variables, and bounds on the values of the control variables. The computational characteristics of the proposed method are demonstrated with two numerical examples. It is shown that optimal initial choice of multipliers is instrumental in increasing the likelihood of convergence of a quasi-linearization algorithm.