Limited Memory BFGS Algorithm Research Articles

Modified subspace limited memory BFGS algorithm for large-scale bound constrained optimization

In this paper, a subspace limited memory BFGS algorithm for solving large-scale bound constrained optimization problems is developed. It is modifications of the subspace limited memory quasi-Newton method proposed by Ni and Yuan [Q. Ni, Y.X. Yuan, A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization, Math. Comput. 66 (1997) 1509–1520]. An important property of our proposed method is that more limited memory BFGS update is used. Under appropriate conditions, the global convergence of the method is established. The implementations of the method on CUTE test problems are presented, which indicate the modifications are beneficial to the performance of the algorithm.

A new subspace limited memory BFGS algorithm for large-scale bound constrained optimization

An active set limited memory BFGS algorithm for large-scale bound constrained optimization is introduced. The active sets are based on guessing technique to be identified at each iteration, the search direction in free subspace is determined by limited memory BFGS (L-BFGS) algorithm, which provides an efficient means for attacking large-scale optimization problems. The implementations of the method on CUTE test problems are described.

Global convergence of QPFTH method for large-scale nonlinear sparse constrained optimization

A QP-free, truncated hybrid (QPFTH) method was proposed and developed in [6] for solving sparse large-scale nonlinear programming problems. In the hybrid method, a truncated Newton method is combined with the method of multiplier. In every iteration level, either a truncated solution for a symmetric system of linear equations is determined by CG algorithm or an unconstrained subproblem is solved by the limited memory BFGS algorithm such that the hybrid algorithm is suitable to large0scale problems. In this paper, the consistency in the hybrid method and a steplength procedure are discussed and developed. The global convergence of QPFTH method is proved and the two-step Q-quadratic convergence rate is further analyzed.