| (1) | Initialization: choose a sample radius , penalty parameter , constraint violation tolerance , sample size p, line search constant , backtracking constant , sample radius reduction factor , penalty parameter reduction factor , constraint violation tolerance reduction factor , infeasibility tolerance , and stationarity tolerance parameter . Choose an initial iterate and set and . | | (2) | Termination conditions check: while , if and , output solution and stop. | | (3) | Adaptive gradient sampling: generate , , and by (22)–(24) and (31). | | (4) | Search direction calculation: choose , solve (14)–(21) to get . | | (5) | L-BFGS update: update by (26) for next iteration. | | (6) | Parameter update: if , then go to step 9. Otherwise, if , set , but if , set . Then, set , , and go to step 8. | | (7) | Line search: set as the largest value in the sequence such that satisfies: and | | (8) | Iteration increment: set and go to step 3. | | (9) | end do |
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