An Advanced Broyden–Fletcher–Goldfarb–Shanno Algorithm for Prediction and Output-Related Fault Monitoring in Case of Outliers

Algorithm 1

BFGS algorithm.

(1)	Give the initial point , the initial quasi-Newton matrix , and the termination limit , iterations .
(2)	If , stop.
(3)	Calculate .
(4)	Let , calculate the score vector , and load vector . Among them, is the column of , and is the column of . The th component of the load vector is calculated. Calculate load vector.
(5)	Find step factor by linear search. Make .
(6)	Correction produces ,
	.
	satisfies the quasi-Newton condition , where
	.
(7)	, go to Step 2.