参数优化的最优性及在控制问题中的一个应用(英文)

OPTIMALITY FOR OPTIMIZATION PROBLEMS WITH PARAMETERS AND AN APPLICATION TO CONTROL PROBLEMS

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条件.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-convexhke, pseudo-invexconvexlike for single-valued with parameters in Banach spaces. Secondly, we prove two sufficient optimality conditions of weak efficient solution in vecter optimization with parameters under this kind of weaker convex conditions. Finally, as an application,we consider a kind of optimal control problems with state constraints.