A splitting method for quadratic programming problem |
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Authors: | Wei Ziluan |
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Institution: | (1) Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080 Beijing, China |
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Abstract: | A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded. |
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Keywords: | Quadratic programming problem matrix splitting method R-linear rate of convergence |
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