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运筹学学报 ›› 2011, Vol. 15 ›› Issue (2): 77-84.

• 运筹学 • 上一篇    下一篇

类不可微优化的Fritz-John条件

潘少荣, 张立卫   

  • 出版日期:2011-06-15 发布日期:2011-06-15
  • 基金资助:

    国家自然科学基金(No. 11071029)

Fritz-John Condition for a Class   of Nondifferntiable Optimization

 PAN  Shao-Rong, ZHANG  Li-Wei   

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

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摘要： 基于星形集空间的性质,定义一类星形可微函数.这类函数是方向可微的,其方向导数可以表示成两个正齐次非负连续函数之差,其星形微分为一星形集对.对于含有不等式约束条件的星形可微优化问题, 给出一个Fritz-John形式的最优性必要条件.

关键词: 不可微优化, 星形集空间, 星形微分, Fritz-John条件

Abstract: Based on the properties of the space of star-shaped sets, a class of star-shaped differentiable functions,whose directional derivatives are representable as a difference of two nonnegative positively homogeneous continuous functions, is defined. The necessary optimality condition of Fritz-John type for an 
optimization problem with star-shaped differentiable inequality constraints is given.

Key words:  cone, branch-and-bound method, global optimization

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