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A limited memory algorithm for bound constrained optimization. (English) Zbl 0836.65080
The authors present an algorithm of solving the nonlinear optimization problems with simple bounds on the variables. It is assumed that the number of variables \(n\) is large, and that a limited storage is available for updating quasi-Newton matrices. The algorithm uses the gradient projection approach to determine the active constraints at each iteration, and the limited memory BFGS matrices represented in the compact form to approximate the Hessian of the objective function such that the computational cost of one iteration can be kept to be of order \(n\).
Numerical tests show that the proposed bound limited memory algorithm has a low computational cost per iteration, modest storage requirements, and it has the ability to solve problems in which the Hessian matrices are large, unstructured, dense, and unavailable.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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