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运筹学学报 ›› 2011, Vol. 15 ›› Issue (2): 11-18.

• 运筹学 • 上一篇    下一篇

无条件C的广义$\alpha \eta $}-单调性的判别标准

 唐万梅,  戎卫东   

  • 出版日期:2011-06-15 发布日期:2011-06-15

Criteria for Generalized \alpha \eta -Monotonicities

TANG Wanmei, RONG Weidong   

  • Online:2011-06-15 Published:2011-06-15
  • Supported by:

    Supported by the Natural Science Foundation of China (No.10771228), the Natural Science Foundation of Chongqing (No. CSTC, 2010BB2090), Education Commission project Research Foundation of Chongqing (No．KJ110617), Chongqing Key Laboratory of Operations Research and System Engineering (No. CSTC, 2006CA8001)

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摘要： 用$\alpha $和 $\eta $关于第一分量是仿射的且是斜对称的条件 代替条件C, 得到如下结论: (1)如果一个函数的梯度是(严格)$\alpha \eta $-伪单调的,则该函 数是(严格)伪$\alpha \eta $-不变凸的; (2)如果一个函数的梯度是拟$\alpha \eta $-单调的,则 该函数是拟$\alpha \eta $-不变凸的.

关键词: 数学规划, 广义\alpha \eta -单调性, 广义\alpha \eta-不变凸函数, 仿射

Abstract: If  $\alpha ~{\rm and}~\eta $ are  affine in the first argument and skew instead of Condition C, the following results are obtained: (i) if the gradient of a function is (strictly) $\alpha \eta $-pseudomonotone,  the function is (strictly) pseudo $\alpha \eta $-invex;  (ii) if the gradient of a function is quasi $\alpha \eta $-monotone,  the  function is quasi $\alpha \eta $-invex.

Key words: mathematical programming, generalized \alpha \eta -monotonicity, generalized \alpha \eta -invex functions, affine

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