Optimality of central and projection algorithms

This paper investigates optimality properties of central and projection algorithms for linear problems in the field of system identification in a context in which uncertainty is described in a deterministic rather than statistical way. Particular attention is devoted to least-squares algorithms when the measurement noise is assumed to be unknown but bounded in a Hilbert norm. A major contribution of this paper consists in proving that least-squares algorithms enjoy strong optimality properties. On the contrary, it is pointed out that these properties do not hold for other frequently used projection algorithms, such as least-absolute-values or minimax algorithms, corresponding to a description of the measurement error in h or l∞ norm, respectively. © 1986.