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.
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Research partially supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the US Department of Energy under grant DE-FG02-86ER25013.A000, and by the US Army Research Office through the Mathematical Sciences Institute, Cornell University.
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Coleman, T.F., Fenyes, P.A. Partitioned quasi-Newton methods for nonlinear equality constrained optimization. Mathematical Programming 53, 17–44 (1992). https://doi.org/10.1007/BF01585692
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DOI: https://doi.org/10.1007/BF01585692