Real-Time Optimization as a Generalized Equation

We establish results for the problem of tracking a time-dependent manifold arising in online nonlinear programming by casting this as a generalized equation. We demonstrate that if points along a solution manifold are consistently strongly regular, it is possible to track the manifold approximately by solving a linear complementarity problem (LCP) at each time step. We derive sufficient conditions that guarantee that the tracking error remains bounded to second order with the size of the time step, even if the LCP is solved only to first-order accuracy. We use these results to derive a fast, augmented Lagrangean tracking algorithm and demonstrate the developments through a numerical case study.



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