The Global Convergence of a Modified BFGS Method under Inexact Line Search for Nonconvex Functions

Algorithm 1

Algorithm MBFGS.

	Step 0: given a point , constants , and an symmetric positive-definite matrix , set .
	Step 1: stop if .
	Step 2: obtain a search direction by solving
	Step 3: calculate using the inequalities (11) and (12).
	Step 4: set .
	Step 5: if holds, then let , , and go to Step 7; otherwise, go to Step 6.
	Step 6: let be defined by (15), , and .
	Step 7: update using formula (10).
	Step 8: let , and go to Step 1.