C-E-凸函数及其在优化问题中的应用

C-E-Convex Function and its Applications in Optimization

提出了一类新的广义凸性:C-E-凸函数,并讨论了C-E-凸函数和C-凸函数之间的关系.给出了相应的择一性定理,并将其用于讨论一类集值优化问题的弱有效解和其标量化问题解的关系.改进和推广了最近文献中相应结果.

E - convexity is an important kind of generalized convexity. C - E - convex function, a new gener- alized convexity, is introduced in the paper, and the relationships between C - E - convex function and C - convex function are discussed. An Alternative Theorem is established under C -E -convex function, and its applications in the set - valued optimization are also discussed. The relationships between the weak efficient solution and the so- lution for its scalarization problem are discussed. The conclusions improve and extend some corresponding results in the recent references.