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• W1882546749 abstract "We describe the outcome of numerical experiments using three approaches for solving convex QP-problems in standard form, namely the unconstrained technique of Kanzow [10], the bound constrained technique of Friedlander, Martinez and Santos [7] and the author’s bound constrained quadratic extended Lagrangian [19]. These three methods solve the problem by a single unconstrained respectively bound constrained minimization. For our test purposes a test generator has been written which generates problems of this type with free choice of the condition number of the reduced Hessian, condition number of matrix of gradients of binding constraints and number of binding constraints. The exact solution is randomly generated. As a minimizer the new limited-memory BFGS-method (for bound constrained problems) of Byrd, Lu, Nocedal and Zhu [2] has been chosen. This allows using exactly the same minimization technology with exactly the same termination criteria to be used for all three approaches. It turns out that any of these methods is in considerable troubles if the QP-problem is only slightly illconditioned. We discuss the reasons why and possible remedies. With respect to computing effort the method of Friedlander et al. turns out to be the best choice. But in all the “black box”-use of LJ_BFGS_B proves to be inefficient. Possible enhancements are indicated. We also shortly discuss the usage of interior point methods as an alternative." @default.
• W1882546749 created "2016-06-24" @default.
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• W1882546749 date "1997-01-01" @default.
• W1882546749 modified "2023-09-24" @default.
• W1882546749 title "Numerical Experiments with Modern Methods for Large Scale QP-Problems" @default.
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• W1882546749 doi "https://doi.org/10.1007/978-3-642-59073-3_22" @default.
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