Specialized fast algorithms for IQC feasibility and optimization problems

Authors:
Chung-Yao Kao;Alexandre Megretski;Ulf JöNsson
Affiliations:
Department of Mathematics, Division of Optimization and Systems Theory, Royal Institute of Technology, Stockholm 10044, Sweden;LIDS, Massachusetts Institute of Technology, Cambridge, MA, USA;Department of Mathematics, Division of Optimization and Systems Theory, Royal Institute of Technology, Stockholm 10044, Sweden
Venue:
Automatica (Journal of IFAC)
Year:
2004

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Abstract

The conventional way to treat integral quadratic constraint (IQC) problems is to transform them into semi-definite programs (SDPs). SDPs can then be solved using interior point methods which have been proven efficient. This approach, however, is not always the most efficient since it introduces additional decision variables to the SDP, and the additional decision variables sometimes largely increase the complexity of the problem. In this paper, we demonstrate how to solve IQC problems by other alternatives. More specifically, we consider two cutting plane algorithms. We will show that in certain cases these cutting plane algorithms can solve IQC problems much faster than the conventional approach. Numerical examples, as well as some explanations from the point of view of computational complexity, are provided to support our point.