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SIAMCO
2010

Real-Time Nonlinear Optimization as a Generalized Equation

8 years 8 months ago
Real-Time Nonlinear Optimization as a Generalized Equation
Abstract. We establish results for the problem of tracking a time-dependent manifold arising in realtime optimization 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. Key words. generalized equations, stability, nonlinear optimization, on-line, complementarity AMS subject classifications. 34B15, 34H05, 49N35, 49N90, 90C06, 90C30, 90C55, 90C59
Victor M. Zavala, Mihai Anitescu
Added 21 May 2011
Updated 21 May 2011
Type Journal
Year 2010
Where SIAMCO
Authors Victor M. Zavala, Mihai Anitescu
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