Real-time nonlinear optimization as a generalized equation

Abstract:

We establish results for the problem of tracking a time-dependent manifold arising in real-time 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. © 2010 Society for Industrial and Applied Mathematics.

Año de publicación:

2010

Keywords:

• stability
• Nonlinear optimization
• COMPLEMENTARITY
• Generalized equations
• Real-time optimization

Fuente:

scopus