锥广义凸性及其在多目标优化问题的最优性条件和对偶性中的应用

This project mainly focuses on the study of cone generalized convexity and its applications in optimality conditions and duality theory of multiobjectvie optimization, the contents of main researches are as follows: (1) We will propose new classes of cone generalized convexity and study their properties; (2) By using various types of cones, we will introduce new constraint qualifications, and use them to derive optimality conditions of multiobjective optimization, in terms of correlation thoeries such as nonsmooth analysis and and varational analysis; (3) Duality results are developed for nonsmooth multiobjective optimization problems, especially converse duality theorems. The implementation and accomplishment of this project not only improve and perfect multiobjectvie optimization theory, but also promote the applications in pratice.

本项目重点研究锥广义凸性及其在多目标优化问题的最优性条件和对偶理论中的应用，主要内容包括：（1）提出新的锥广义凸性并研究其性质；（2）利用各种锥提出新的约束品性，结合非光滑分析和变分分析等相关理论建立多目标优化问题的最优性条件;（3）非光滑多目标优化问题的对偶性研究，重点是建立逆对偶定理。本项目的实施和完成不仅能丰富和完善多目标优化理论，而且也能促进在实际中的应用。

本项目研究锥广义凸性及其在多目标优化问题的最优性条件和对偶理论中的应用。我们按照预期计划主要研究了：新的广义凸性及其性质；新的约束品性；多目标优化问题的最优性条件；多目标优化问题的对偶性等。此外，我们考虑了一类新的近似真有效解。这些结果丰富和完善了多目标优化理论。本项目取得了一些成果，发表或接收论文6篇，其中SCI论文3篇。同时在该项目的支持下项目主持人获得了国家自然科学基金青年项目，且项目主持人入选“2017年中国（重庆）新加坡博士后国际培养交流计划”。