Optimisation with parametric uncertainty: an ADMM approach

Conference item

To solve convex optimisation problems we rely on iterative algorithms, but when the problem contains parameters that need to be estimated from measurements with noise, another iterative process is needed to perform estimation. In this paper we devise a modified version of the Alternating Direction Method of Multipliers (ADMM) that performs parameter estimation simultaneously with optimisation. Given a convergent parameter estimate, and assuming that the cost function can be expressed in terms of a multi-parametric quadratic program (mp-QP), we prove convergence of the objective values, dual variables and primal residual. Simulation results show that the rate of convergence tracks that of the estimator up to an upper limit that is characterised by convergence rate of ADMM with no parametric uncertainty.

Authors: Pan, Z; Cannon, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: IFAC-PapersOnLine
• Volume: 56
• Issue: 2
• Pages: 1932-1936
• Publication date: 2023-11-22
• Acceptance date: 2022-06-12
• Event title: 22nd World Congress of the International Federation of Automatic Control (IFAC 2023)
• Event location: Yokohama, Japan
• Event website: https://www.ifac2023.org/
• Event start date: 2023-07-09
• Event end date: 2023-07-14
• DOI: 10.1016/j.ifacol.2023.10.1084
• EISSN: 2405-8963
• Language: English
• Keywords: uncertain systems; FFR; convex optimisation; distributed control and estimation