论文标题
使用惩罚和半齿牛顿方法找到一些反向最佳控制问题的全球解决方案
Finding global solutions of some inverse optimal control problems using penalization and semismooth Newton methods
论文作者
论文摘要
我们提出了一种解决特殊的参数识别问题的方法，以解决椭圆形的最佳控制问题到全球最优性。双重问题通过低级问题的最佳价值函数进行了重新制定。重新制定的问题是非凸，违反了鲁滨逊CQ等标准规律性条件。通过放松约束，可以将问题分解为凸问题的家族，这是解决方案算法的基础。分析收敛属性。结果表明，可以采用惩罚方法来解决这一问题，同时保持收敛速度。对于一个示例问题，将身份用作惩罚功能允许通过半齿牛顿方法进行解决方案。提出了数值结果。讨论了我们解决非概念问题的困难和局限性。
We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem. The reformulated problem is nonconvex and standard regularity conditions like Robinson's CQ are violated. Via a relaxation of the constraints, the problem can be decomposed into a family of convex problems and this is the basis for a solution algorithm. The convergence properties are analyzed. It is shown that a penalty method can be employed to solve this family of problems while maintaining convergence speed. For an example problem, the use of the identity as penalty function allows for the solution by a semismooth Newton method. Numerical results are presented. Difficulties and limitations of our approach to solve a nonconvex problem to global optimality are discussed.
