多目标集值优化理论及其进展

Multiobjective set-valued optimization theory and its development

比较系统的介绍了多目标集值优化这一学科,并从(1)标量化问题;(2)不带导数的最优性条件;(3)带导数的最优性条件——FritzJohn及Kuhn-Tucker条件;(4)对偶问题;(5)非光滑分析法;(6)稳定性与灵敏度分析;(7)极大极小定理;(8)集到集映射的优化问题8个方面对这一领域的研究进展情况及所用方法做了较为系统的总结与研究。

The subject of multiobjective set-valued optimization is systemly introduced.The sur- vey involves (1 ) scalar problem;(2 ) the optimality conditions without derivatives;(3 ) the optimality conditions with derivatives;(4) the duality problems;(5) nonsmooth analysis;(6 ) the stability and sensitivity;(7) minimax theorem;(8) the multiobjective optimization of setto set,eight parts.More- over,gives some unsolved problems.