| GLOBAL CONVERGENCE OF QPFTH METHOD FOR LARGE-SCALE NONLINEAR SPARSE CONSTRAINED OPTIMIZATION |
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| 引用本文： | 倪勤. GLOBAL CONVERGENCE OF QPFTH METHOD FOR LARGE-SCALE NONLINEAR SPARSE CONSTRAINED OPTIMIZATION[J]. 应用数学学报(英文版), 1998, 14(3): 271-283. DOI: 10.1007/BF02677409 |
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| 作者姓名： | 倪勤 |
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| 作者单位： | College of Science，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China |
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| 摘 要： | 1.IntroductionIn[6],aQPFTHmethodwasproposedforsolvingthefollowingnonlinearprogrammingproblemwherefunctionsf:R"-- RIandgi:R"-- R',jeJaretwicecontinuouslydifferentiable.TheQPFTHalgorithmwasdevelopedforsolvingsparselarge-scaleproblem(l.l)andwastwo-stepQ-quadraticallyandR-quadraticallyconvergent(see[6]).Theglobalconvergenceofthisalgorithmisdiscussedindetailinthispaper.Forthefollowinginvestigationwerequiresomenotationsandassumptions.TheLagrangianofproblem(1.1)isdefinedbyFOundationofJiangs…
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| 收稿时间： | 1995-04-21 |
Global convergence of QPFTH method for large-scale nonlinear sparse constrained optimization |
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| Ni Qin. Global convergence of QPFTH method for large-scale nonlinear sparse constrained optimization[J]. Acta Mathematicae Applicatae Sinica, 1998, 14(3): 271-283. DOI: 10.1007/BF02677409 |
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| Authors: | Ni Qin |
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| Affiliation: | (1) College of Science, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China |
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| Abstract: | A QP-free, truncated hybrid (QPFTH) method was proposed and developed in [6] forsolving sparse large-scale nonlinear programming problems. In the hybrid method, a truncatedNewton method is combined with the method of multiplier. In every iteration level, either atruncated solution for a symmetric system of linear equations is determined by CG algorithmor an unconstrained subproblem is solved by the limited memory BFGS algorithm such thatthe hybrid algorithm is suitable to large-scale problems. In this paper, the consistency in thehybrid method and a steplength procedure are discussed and developed. The global convergenceof QPFTH method is proved and the two-step Q-quadratic convergence rate is further analyzed. |
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| Keywords: | : Largesscale optimization global convergence sparse problem |
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