| 摘要: |
| 本文主要研究了一类非光滑齐次优化问题(HOP).通过运用Clarke次微分的广义欧拉恒等式获得了使得(HOP)问题的最优解成为KKT点的充分条件并给出了(HOP)问题与(HOP)问题的KKT点及最优解之间的等价刻画.本文的结果是文[1]中已有结果的推广.文中还举例说明了结果的正确性. |
| 关键词: Clarke次微分 KKT点 欧拉恒等式 非光滑齐次优化问题 |
| DOI： |
| 分类号:O177.92 |
| 基金项目:Supported by Scientific Research Foundation of Yunnan Provincial Education Department (2013Y082);Supported by the National Natural Science Foundation of China (11161025). |
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| ON SOME NONSMOOTH HOMOGENEOUS OPTIMIZATION PROBLEMS IN BANACH SPACES |
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ZHANG Juan1, LI Shu-min2
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1.Dpt. of Engineering, Oxbridge College, Kunming University of Science and Technology, Kunming 650106, China;2.Dpt. of Appl. Math., Kunming University of Science and Technology, Kunming 650404, China
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| Abstract: |
| In this paper, we mainly consider the nonsmooth homogeneous optimization problem (HOP). By using the generalized Euler identity for Clarke's subdifferential, a sufficient condition for an optimal solution of (HOP) to be a KKT point is obtained. Moreover, we also give an equivalent characterization of KKT points (optimal solutions) of (HOP) and (HOP), which extend previous ones in[1]. Examples are also given to illustrate our results. |
| Key words: Clarke subdifferential KKT point Euler identity nonsmooth homogeneous optimization problem |
