Partitioned quasi-Newton methods for nonlinear equality constrained optimization

The authors derive new quasi-Newton updates for the (nonlinear) equality constrained minimization problem. The new updates satisfy a quasi-Newton equation, maintain positive definiteness on the null space of the active constraint matrix, and satisfy a minimum change condition. The application of the updates is not restricted to a small neighbourhood of the solution. In addition to derivation and motivational remarks, the authors discuss various numerical subtleties and provide results of numerical experiments.