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A new subspace limited memory BFGS algorithm for large-scale bound constrained optimization. (English) Zbl 1114.65069
A new algorithm that combines an active set strategy with the gradient projection method is presented. As in the work by F. Facchinei, S. Lucidi and L. Palagi [SIAM J. Opt., 12, 1100–1125 (2002; Zbl 1035.90103)] the authors avoid the necessity of finding an exact minimizer of a quadratic subproblem with bound constraints. The algorithm has the following properties: All iterates are feasible and the sequence of the objective function values is decreasing; rapid changes in the active set are allowed; a global convergence theory is established.
Moreover, it reserves the advantage of the effective active set identified technique by Facchinei, Lucidi and Palagi [loc. cit.] and uses the superiority of the subspace limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) method [see Q. Ni and Y. X. Yuan, Math. Comp., 66, 1509–1520 (1997; Zbl 0886.65065)] which has been proved much suit for solving large-scale problems. Namely, the active sets are based on a guessing technique to be identified at each iteration, the search direction in the free subspace is determined by a limited memory BFGS algorithm, which provides an efficient means for attacking large-scale optimizatuin problems. The implementations of the method on CUTE test problems are described.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C06 Large-scale problems in mathematical programming
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