An Accelerated Fixed-Point Algorithm Applied to Quadratic Convex Separable Knapsack Problems

Algorithm 4

FPA2-Aitken algorithm.

	Step 0 (Initialization)
	Set k = 0. Let according to [2, 6, 12].
	Step 1 (Calculating dual bounds)
	For ,
	Compute .
	Step 2 (Calculating fixed-point sums and defining )
	Compute , and using according to FPA2 algorithm.
	Compute .
	Step 3 (Check stopping criterion)
	If , then set according to equations (30) and (33) and STOP.
	Step 4 (Calculating fixed-point sums and defining )
	Compute , and using according to FPA2 algorithm.
	Compute .
	Step 5 (Calculating Aitken acceleration procedure)
	Compute .
	Step 7 (Check stopping criterion)
	If , then set according to equations (30) and (33) and STOP. Otherwise, set and return to Step 2.