SIAM Journal on Scientific Computing · 1995 · 6.2K citations · 15 references
Natural SciencesComputer ScienceMathematicsAlgorithmsOptimizationTheory Of ComputationApproximation AlgorithmsConstrained OptimizationGradient-based OptimizationLarge-scale OptimizationNonlinear ProgrammingOptimization TheoryGradient Method OptimizationHessian ApproximationLarge-scale Nonlinear ProgrammingMemory-bounded AlgorithmsNonlinear OptimizationObjective Function FormulationOptimization Algorithms
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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Updating quasi-Newton matrices with limited storage
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Constrained minimization methods
E. S. Levitin, B. T. Polyak · USSR Computational Mathematics and Mathematical Physics · 1966 · 852 citations