| A MINIMIZING ALGORITHM FOR COMPLEX NONCONVEX NONDIFFERENTIABLE FUNCTIONS |
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| 引用本文： | XUCHENGXIAN CHENZHIPING. A MINIMIZING ALGORITHM FOR COMPLEX NONCONVEX NONDIFFERENTIABLE FUNCTIONS[J]. 高校应用数学学报(英文版), 1995, 10(2): 141-154. DOI: 10.1007/BF02662858 |
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| 作者姓名： | XUCHENGXIAN CHENZHIPING |
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| 作者单位： | DepartmentofMathematics,Xi＇anJiaotongUniversity,Xi＇an710049 |
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| 摘 要： | The minimization of nonconvex, nondifferentiable functions that are compositions of max-type functions formed by nondifferentiable convex functions is discussed in this paper. It is closely related to practical engineering problems. By utilizing the globality of ε-subdifferential and the theory of quasidifferential, and by introducing a new scheme which selects several search directions and consider them simultaneously at each iteration, a minimizing algorithm is derived. It is simple in structure, implementable, numerically efficient and has global convergence. The shortcomings of the existing algorithms are thus overcome both in theory and in application.
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| 关 键 词： | 完全非凸不可微函数 极小化算法 全局收敛性 光滑函数 优选法 |
| 收稿时间： | 1993-11-17 |
A minimizing algorithm for complex nonconvex nondifferentiable functions |
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| Xu Chengxian,Chen Zhiping. A minimizing algorithm for complex nonconvex nondifferentiable functions[J]. Applied Mathematics A Journal of Chinese Universities, 1995, 10(2): 141-154. DOI: 10.1007/BF02662858 |
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| Authors: | Xu Chengxian Chen Zhiping |
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| Affiliation: | XU CHENGXIAN AND CHEN ZHIPING |
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| Abstract: | The minimization of nonconvex, nondifferentiable functions that are compositions of max-type functions formed by nondifferentiable convex functions is discussed in this paper. It is closely related to practical engineering problems. By utilizing the globality of ε-subdifferential and the theory of quasidifferential, and by introducing a new scheme which selects several search directions and consider them simultaneously at each iteration, a minimizing algorithm is derived. It is simple in structure, implementable, numerically efficient and has global convergence. The shortcomings of the existing algorithms are thus overcome both in theory and in application. |
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| Keywords: | Quasidifferentiable subdifferential stability global convergence. |
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