A limited memory algorithm for bound constrained optimization
TL;DR: An algorithm for solving large nonlinear optimization problems with simple bounds is described, based on the gradient projection method and uses a limited memory BFGS matrix to approximate the Hessian of the objective function.
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Abstract: An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based on the gradient projection method and uses a limited memory BFGS matrix to approximate the Hessian of the objective function. It is shown how to take advantage of the form of the limited memory approximation to implement the algorithm efficiently. The results of numerical tests on a set of large problems are reported.
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References
Global convergence of a class of trust region algorithms for optimization with simple bounds
TL;DR: It is shown that, when the strict complementarily condition holds, the proposed algorithms reduce to an unconstrained calculation after finitely many iterations, allowing a fast asymptotic rate of convergence.
Projected Newton methods for optimization problems with simple constraints
Dimitri P. Bertsekas
- 01 Dec 1981
TL;DR: It is shown that Dk can be calculated simply on the basis of second derivatives of f so that the resulting Newton-like algorithm has a typically superlinear rate of convergence.