一类广义凸多目标规划问题研究

首先引入了涉及高阶强Pre-invex函数的多目标优化问题m阶严格局部极小元的定义,在此基础上讨论了多目标优化问题的优化条件,最后研究了变分不等式的解与多目标优化问题高阶严格极小元之间的关系,其变分不等式的解正是多目标优化问题的高阶严格极小元,这些研究内容推广了Guneer-Bhatia给出的相关结论.

Study on a Class of Multiobjective Programming under Generalized Convexity

In this paper,we introduce the definition of m-order strict local minimum element for multiobjective optimization problem involving higher order strong Pre-invex function.On this basis,the optimization conditions of multi-objective optimization problems are discussed.Finally,the relationship between the solutions of variational inequalities and the higher-order strict minimal elements of multi-objective optimization problems is studied.The solutions of variational inequalities are exact high-order strictly minimal elements for multi-objective optimization problems.These results extend the relevant conclusions given by GuneerBhatia.