Global Convergence of a Modified Two-Parameter Scaled BFGS Method with Yuan-Wei-Lu Line Search for Unconstrained Optimization

Algorithm 1

A modified two parameter scaled BFGS algorithm—MTPSBFGS.

	Step 1: given an initial point , an symmetric positive definite matrix , is sufficiently small and choose constants , , and . Set .
	Step 2: if , stop.
	Step 3: obtain a search direction by solving
	Step 4: compute by Yuan-Wei-Lu line search conditions (22) and (23).
	Step 5: find the scaling factors and by (18) and (19).
	Step 6: let . Update by (17).
	Step 7: let , and go to Step 2.