广义向量最优化问题的 Mond-Weir 型对偶

对广义向量最优化问题建立了Ｍｏｎｄ＿Ｗｅｉｒ型对偶，证明了原问题和对偶问题之间的弱对偶定理、直接对偶定理和逆对偶定理。

电镀产品的公差与二元变闭曲线

从常数到变量的飞跃,从定曲面到变曲面的探索,前景乐观.本文由电镀并简化为二维情形引出含双参量的变化闭曲线.通过建立法微分等概念,使变闭曲线的变化性状可用多元微分加以处理,建立了电镀公差估计及优化参数的微分基础,并导出有关性质.

集值优化问题的Benson真有效解的广义导数型最优性条件

引进了集值映射关于锥的Clarke切导数, Adjacent切导数与Contingent切导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义导数型最优性条件．

一类新的二阶切导数及其在集值优化中的应用

提出了一种新的二阶切锥,讨论了它与二阶广义相依切集的关系.利用此锥定义了一种新的二阶切导数,讨论了它与二阶广义相依上图切导数的关系.利用Henig扩张锥的性质,给出了集值优化在Henig有效元意义下的二阶最优性必要条件.在近似锥-次类凸假设下给出了Benson真有效元意义下的二阶最优性必要条件.举例说明了本文的主要结论.

On Relations of Vector Optimization Results with C^(1,1) Data

In this article we prove that some of the sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Luc [Appl. Math., 51, 5-36 （2006）] generalize （strictly） those presented by Guerraggio, Luc [J. Optim. Theory Appl., 109, 615-629 （2001）]. While the former paper shows examples for which the conditions given there are effective but the ones from the latter paper fail, it does not prove that generally the conditions it proposes are stronger. In the present note we complete this comparison with the lacking proof.