摘要:在Banach空间中,给出了含参数的单值映射的不变类凸,拟不变类凸和伪不变类凸的概念.在这类较弱凸性条件下,提出了参数优化问题弱有效解的几个最优性充分务件.作为应用,研究了一类状态约束最优控制问题的弱最优控制.%Firstly,we introduce the concept of Adjacent derivative,invex-convexlike,quasi-invex-convexlike,pseudo-invex-convexlike for single-valued with parameters in Banach spaces.Secondly,we prove two sufficient optimality conditions ofweak efficient solution in vecter optimization with parameters under this kind of weaker convex conditions.Finally.as.an ap-plication,We comider a kind of optimal control problems with slate constraints.