中文

Operations Research Transactions ›› 2012, Vol. 16 ›› Issue (2): 1-8.

• Original Articles •     Next Articles

Convex function| sub-b-convex set|  sub-b-convex function| pseudo-sub-b-convex function| optimality conditions

CHAO Miantao1,2, JIAN Jinbao3 , LIANG  Dongying4   

  1. 1.  College of Applied Sciences, Beijing University of Technology, Beijing 100124, China; 2. Department of Mathematics and Computer Science, Guangxi College of Education, Nanning 530023, China; 3. College of Mathematics and Information Science, Guangxi University, Nanning 530004,  China; 4. Guangxi Vocational and Technical College of Communications, Nanning 530023,  China
  • Received:2011-05-30 Revised:2011-08-21 Online:2012-06-15 Published:2012-06-15
  • Supported by:

    National Science Foundation of China

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Abstract: The paper studied a new generalized convex function which called sub-b-convex function, and introduced a new concept of sub-b-convex set. The basic roperties of sub-b-convex functions were discussed in general case and differentiable case, respectively. And, obtained the sufficient conditions that the sub-b-convex function become quasi-convex function or pseudo-convex function. Furthermore, the sufficient conditions of optimality for unconstrained and inequality constrained programming were obtained under the sub-b-convexity.

Key words: convex function, sub-b-convex set, sub-b-convex function, pseudo-sub-b-convex function, optimality conditions