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A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization. (English) Zbl 0886.65065

The following nonlinear programming problem with simple bounds on variables

minimizef(x)subjecttoxu

is considered. The objective function f(x) is assumed to be twice continuously differentiable, and u are given bound vectors in n , and n is the number of variables, which is assumed to be large.

The given subspace limited memory quasi-Newton algorithm does not need to solve any subproblems. The search direction of the algorithm consists of three parts: a subspace quasi-Newton direction, and two subspace gradient and modified gradient directions. The global convergence of the method is proved and some numerical results are given.


MSC:
65K05Mathematical programming (numerical methods)
90C06Large-scale problems (mathematical programming)
90C30Nonlinear programming