【摘要】 研究一类含有支撑函数的多目标规划问题，以弧连通凸函数的广义凸性理论为基础构建最优性条件。提出了一类新的H不变凸函数，运用H不变凸函数，针对一类多目标规划问题的解展开研究，借助新的凸性，得到了H不变凸函数最优性条件、H拟凸函数最优性充分条件以及H伪凸函数最优性条件。研究结果对H不变凸函数的最优性条件进行了推广。更多还原

【Abstract】 This paper investigates a class of multi-objective programming problems involving support functions, based on the generalized convexity theory of arcwise connected convex functions, optimality conditions are established. A novel class of H-invariant convex functions is introduced, and their application to the solutions of a specific class of multi-objective programming problems is explored. Leveraging this new convexity notion, optimality conditions for H-invariant convex functions are derived, along with sufficient optimality conditions for H-quasiconvex functions and optimality conditions for H-pseudo-convex functions, thereby extending the existing optimality conditions for H-invariant convex functions.更多还原