| THE CONVERGENCE OF BROYDEN ALGORITHMSWITHOUT CONVEXITY ASSUMPTION |
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| 作者姓名： | PU Dingguo |
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| 作者单位： | Institute of Applied Mathematics，Shanghai Tiedao University，Shanghai 200333，China |
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| 摘 要： | 1.IatroductionWeknowthatthevariablemetricalgorithms,suchastheBroydenalgorithms1],areveryusefulandefficientmethodsforsolvingthenonlinearprogrammingproblem:min{f(x);xERn}.(1.1)Withexactlinesearch,Powelll2]provedthattherateofconvergenceofthesealgorithmsisone-stepsuperlinearfortheuniformlyconvexobjectivefunction,andifthepoiedsgivenbythesealgorithmsareconvergeal,PnandYul3]provedthattheyaregloballyconvergelitforthecolltinuousdifferentiablefunction.Withoutexactlinesearchseveralresultshavebeenobtai…
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THE CONVERGENCE OF BROYDEN ALGORITHMS WITHOUT CONVEXITY ASSUMPTION |
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| PU Dingguo.THE CONVERGENCE OF BROYDEN ALGORITHMSWITHOUT CONVEXITY ASSUMPTION[J].Journal of Systems Science and Complexity,1997(4). |
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| Authors: | PU Dingguo |
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| Abstract: | In this paper we discuss the convergence of the Broyden algorithms withoutconvexity and exact line search assumptions. We proved that if the objective function issuitably smooth and the algorithm produces a convergent point sequence, then the limitpoint of the sequence is a critical point of the objective function. |
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| Keywords: | Broyden algorithms convergence convexity exact line search |
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