具有抽象约束的l-稳定函数的多目标优化问题的二阶充分条件  

On second-order sufficient conditions in abstract constrained multiobjective optimization problem with l-stable function

作　　者：王凤玲[1] 宋文[1] 

机构地区：[1]哈尔滨师范大学数学系

出　　处：《黑龙江大学自然科学学报》2009年第4期465-468,共4页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省杰出青年基金资助项目(JC200707)

摘　　要：对于多目标优化问题而言,二阶最优性条件在优化理论中占有非常重要的地位,尤其是多目标问题的二阶充分条件,因为它能保证求得的解确实是原问题的有效解。在已有的无约束l-稳定函数多目标优化问题的二阶充分条件的基础上,借助定向距离函数和l-稳定函数的性质及引入的广义二阶Peano(Dini)方向导数,进一步刻画了具有抽象约束的l-稳定函数的多目标优化问题的二阶孤立极小点的二阶充分条件。For multi - objective optimization problems, the second - order optimality conditions in optimization theory plays a very important position, especially the second - order sufficient conditions in multi - objective problems, for it ensures the solution which is indeed an effective solution to the original questions. On the basic that existing second - order sufficient condition for an isolated minimizer of order 2 for unconstrained multi - objective optimization, using the so called ＂oriented distance＂ from a point to a set, l - stable function and generalized second - order Peano（Dini） direction derivative, some second -order sufficient conditions for an isolated minimizer of order 2 for constrained muhiobjective optimization problems with l-stable functions are obtained.

关 键 词：多目标问题 l-稳定函数 广义二阶Peano(Dini)方向导数 二阶充分条件 二阶孤 立极小点 

分 类 号：O189.1[理学—数学]