带变动指标集的非光滑半无限优化问题的最优性条件研究

Semi-infinite optimization with variable index as a model of generalized semi-infinite optimization has wide applications in various areas such as economics and finance, engineer design, computational biology and medicine. It has attracted extensive attention in recent years as it enjoys exclusive structure features different from the standard semi-infinite optimization problems. This project concentrates on the study of the theory for nonsmooth semi-infinite optimization with variable index. We mainly consider optimality conditions of the semi-infinite optimization with variable index after transforming it as an ordinary optimization problems either by using the optimal value functions or the penalty functions of the lower level problems or using the symmetrical representation formula of the closure of the feasible set of semi-infinite optimization with variable index. This project is scientifically significant and extremely valuable, not only for providing new theory and methods for semi-infinite optimization with variable index and but also for enriching optimization theory.

带变动指标集的半无限优化问题是半无限优化模型的推广和发展，在经济金融、工程设计、计算生物以及医药等诸多领域有着广泛的应用。相对于标准半无限优化，对该类问题的研究起步较晚，且该类问题有很多特性，因而近年来逐步受到关注。本项目主要借助非光滑和变分分析工具，围绕带变动指标集的非光滑半无限优化问题的理论进行研究。具体研究内容如下：（1）通过下层问题的值函数或罚函数将模型转换为非线性优化问题，进而利用变分分析工具来刻画模型解的最优性条件；（2）在基于模型可行集结构情况下，将模型松弛为其可行集闭包上的优化问题，进而研究解的性质以及最优性条件。本项目的实施可为求解带变动指标集的半无限优化问题提供新的方法，不仅可丰富和发展半无限优化研究理论，而且有助于解决一些产生于工程、经济、生物、医药等领域的实际问题。