Performance Analysis of Trust Region Subproblem Solvers for Limited-Memory Distributed BFGS Optimization Method

The limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method performs very efficiently for large-scale problems. A trust region search generally more and robustly than a line method, especially when the gradient of objective function cannot be accurately evaluated. computational cost an L-BFGS subproblem (TRS) solver depend mainly on number unknown variables ( n ) variable shift vectors change m used Hessian updating, with << In this paper, we analyze performances different methods to solve TRS. first is direct using Newton-Raphson (DNR) Cholesky factorization dense × matrix, second one based inverse quadratic (DIQ) interpolation, third new that combines matrix inversion lemma (MIL) approach update associated matrices vectors. MIL applied reduce dimension original problem variables. Instead directly expensive matrix-matrix matrix-vector multiplications TRS, efficient employed iteratively. TRS DNR or DIQ method. Testing representative suite problems indicates can converge optimal solutions comparable those obtained Its represents only modest overhead over well-known line-search but delivers improved stability in presence inaccurate gradients. When compared by factor proportional n2/m