@article{iiasa14072,
          volume = {20},
          number = {4},
           title = {On the local and global convergence of a reduced Quasi-Newton method1},
       publisher = {Taylor and Francis Ltd.},
         journal = {Optimization},
             doi = {10.1080/02331938908843462},
           pages = {421--450},
            year = {1989},
             url = {https://pure.iiasa.ac.at/id/eprint/14072/},
            issn = {0233-1934},
        abstract = {In optimization in Rn with m nonlinear equality constraints, we study the local convergence of reduced quasi-newton methods, in which the updated matrix is of order n-m. Furthermore, we give necessary and sufficient conditions for superlinear convergence (in one step) and we introduce a device to globalize the local algorithm. It consists in determining a step along an arc in order to decrease an exact penalty function and we give conditions so that asymptotically the step-size will be equal to one. {\copyright} 1989, Taylor \& Francis Group, LLC.},
          author = {Gilbert, J.-C.}
}