在广义凸性条件下，建立了弱对偶性定理。
Weak duality theorem is established under generalized convexity conditions.
函数的凸性与广义凸性在数学规划以及最优化理论中起着非常重要的作用。
Convexity and generalized convexity of functions play an important role in mathematical programming and optimal theory.
并在广义凸性和广义单调性的条件下，给出了隐向量均衡问题的解的存在性。
In addition, under the generalized convexity and generalized monotonicity, solution existence for implicit vector equilibrium problems is investigated.
而最优化理论的许多有意义的重要结果大都建立在凸性和某些广义凸性的假定上。
And many meaningful and important results in the optimization theory was base on the the convex and some assumptions on the convexity.
接着，利用函数的上次微分构造了不可微向量优化问题（VP）的广义对偶模型，并且在适当的弱凸性条件下建立了弱对偶定理。
Finally, the generalized dual model of the problem (VP) is presented with the help of upper subdifferential of function, and a weak duality theorem is given.
本文研究一类广义负系数单叶解析函数，得到了准确的系数估计，偏差定理，凸性半径和星形性半径。
In this paper, we study a generalized class of univalent functions with negative coefficients. Sharp coefficient estimates, distortion theorem and radius of convexity and starlikeness are obtained.
然后，在实线性空间中建立了一个广义次似凸集值映射的择一性定理。
Then, a theorem of the alternative for generalized subconvexlike set valued maps in real linear spaces is established.
引进了相对内部，应用凸集分离定理建立了一个广义凸集值映射的择一性定理。
Then relative interior is introduced and an alternative theorem of generalized convex set-valued maps is established by using the separation theorem.
最后，利用择一性定理，获得了含不等式和等式约束的广义次似凸集值映射向量最优化问题的最优性条件。
Finally, the optimality conditions for vector optimization problems with set valued maps with equality and inequality constraints are obtained with it.
最后，利用择一性定理，获得了含不等式和等式约束的广义次似凸集值映射向量最优化问题的最优性条件。
Finally, the optimality conditions for vector optimization problems with set valued maps with equality and inequality constraints are obtained with it.
应用推荐