Inexact SCP Methods for Hierarchical Optimization of Decomposable Systems

Abstract:

We discuss how Sequential Convex Programming (SCP) Methods with inexact derivatives can be used to address the hierarchical optimization of large decomposable systems. It is assumed that detailed "local" sub-system models exist and can be evaluated, that are, however, not available to the central optimizer. The "central" higher level optimization algorithm only has a crude model of the sub-systems and their interactions with each other. The aim is to design an overall algorithm that converges to a centrally optimal solution, or at least to a feasible solution, which respects all constraints despite the fact that the detailed subsystem interactions are unknown to the central optimizer. The central optimizer only solves a medium scale convex problem in each iteration of the algorithm, while the subsystems perform only some function evaluations, and possibly adjoint derivatives.

Though our motivation are optimal control applications of interconnected systems, we regard a large but finite dimensional nonlinear optimization problem, and show how the hierarchical and distributed algorithm that exchanges only vector information between the subsystems and with the higher level can converge to a local solution of the centralized problem if a suitable coarse model of the problem exists. When the converging method is applied to a convex problem, it will converge to a global solution. The talk presents recent algorithmic ideas rather than a fully tested algorithm, so only some motivational examples are presented from within the EU FP7 project "HD-MPC - Hierarchical and Distributed Model Predictive Control".

Joint work with A. Kozma, C. Savorgnan, B. Houska, Quoc Tran Dinh.

 Slides

Biography:

• since 2006: Associate professor at Electrical Engineering Department of  K.U. Leuven,  Belgium, and Principal investigator of the Optimization in Engineering Center OPTEC.
• 2001-2006: postdoctoral stays at IWR Heidelberg, IMA Minneapolis, INRIA Rocquencourt, UPS Toulouse.
• 1999-2001: PhD in scientific computing at IWR, Heidelberg University
• 1993-99: Studies of Physics and Mathematics in Heidelberg and Cambridge (UK).
• Born in 1971 in Hamburg, Germany