Superlinearly convergent quasi-newton algorithms for nonlinearly constrained optimization problems

A class of algorithms for nonlinearly constrained optimization problems is proposed. The subproblems of the algorithms are linearly constrained quadratic minimization problems which contain an updated estimate of the Hessian of the Lagrangian. Under suitable conditions and updating schemes local convergence and a superlinear rate of convergence are established. The convergence proofs require among other things twice differentiable objective and constraint functions, while the calculations use only first derivative data. Rapid convergence has been obtained in a number of test problems by using a program based on the algorithms proposed here.Research supported by NSF Grant GJ-35292 at the University of Wisconsin.