### LANS Publications

# "Real-Time Optimization as a Generalized Equation"

V. M. Zavala and M. Anitescu

*SIAM J. Control Optim.*, vol. 48, , pp. 5444-5454. Also Preprint ANL/MCS-P1641-0609

Preprint Version: [pdf]

We establish results for the problem of tracking a time-dependent manifold arising in on-line nonlinear programming by casting this as a parametric 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 single linear complementarity problem (LCP) at each time step. We derive sufficient conditions guaranteeing that the tracking error remains bounded to second order with the size of the time step, even if the LCP is solved only approximately. We use these results to derive a fast, augmented Lagrangian tracking algorithm and demonstrate the developments through a numerical case study.