Abstract: This paper presents a new function minimization algorithm for minimizing nonlinear functions of a finite number of variables subject to nonlinear equality constraints. The algorithm also provides for the explicit handling of upper and lower bounds on each of the independent variables. Although other more general inequality constraint can be transformed into an equality constraint at the expense of introducing an additional slack variable. The algorithm proposed combines the idea of a "balance function," developed independently in References 1 and 2 with a second order method for updating the balance function La grange multipliers originally developed in Reference 3. This updating technique makes use of the current estimate of the inverse Hessian of the balance function which is a byproduct of the unconstrained minimization of the balance function using the Fletcher-Powell algorithm.