| The Structure of Clarke's Generalized Gradient andComputing Some of Its Element for the SmoothComposition of Max-Type Functions |
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| 作者姓名： | YAN GAO |
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| 作者单位： | Department of Applied Mathematics，Dalian University of Technology，Dalian 116024，China |
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| 摘 要： | 1.IntroductionConsidersmoothcompositionsofmax-typefunctionsoftheform:f(x)=g(x,aestfij(x),',,T?:fmj(x)),(1.1)wherexER",Ji,i~1,',marefiniteindexsets,gandfij,jEJi,i=1,',marecontinuouslydifferentiableonRill 71andR;'respectively.Thisclassofnonsmoothfunct…
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The Structure of Clarke's Generalized Gradient and Computing Some of Its Element for the Smooth Composition of Max-Type Functions |
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| YAN GAO.The Structure of Clarke's Generalized Gradient andComputing Some of Its Element for the SmoothComposition of Max-Type Functions[J].OR Transactions,1997(2). |
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| Authors: | YAN GAO |
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| Abstract: | Clarke's generalized gradient of the smooth composition of max-type functions isconsidered. Clarke's generalized gradient of this class of functions is a convex hull of afinite number of points. Several elements of Clarke's generalized gradient is computed.Computing elements of Clarke's generalized gradient for this class of functions, at apoint, is transformed into computing gradients of a smooth function, at a point, bydetermining the compatibility of systems of linear inequalities. |
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| Keywords: | Clarke's generalized gradient Max-type function Lipschitzian function quasidifferentiable function nonsmooth optimization |
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