摘要
A first-order necessary condition for an infinite-dimensional nonlinear op-timization problem, which arises when the all-at-once method is employed to slove theoptimal control problems, is formulated and analyzed. Operator constraint and simplebound on part of the variables are both considered. Based on this optimality condition,the trust-region subproblems are built, then the trust region method rnay be employedto deal with the optimizatiou problem in infinite-dimensional space.
本文给出了当all-at-once方法用于求解最优控制问题而产生的一类同时具有算子和对部分变量具有简单界约束的无穷维最优化问题的一个一阶必要条件,构造了相应的信赖域子问题,据此,信赖域法可以用于求解无穷空间中的最优化问题。
