Partitioned Quasi-Newton Methods for Nonlinear Equality Constrained Optimization

Abstract

We 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, we discuss various numerical subtleties and provide results of numerical experiments.