用于松弛型逆最优控制问题的罚类型方法
A penalty-type method for relaxed inverse optimal control problems
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中文总结 AI 辅助
本文提出一种罚类型方法，用于处理逆最优控制产生的双层优化问题，可计算松弛值函数重述的驻点，无需线搜索，收敛性有保证，数值实验验证了其有效性。
中文摘要 AI 辅助
本文致力于引入并分析一种罚类型方法，用于数值处理由逆最优控制产生的一类双层优化问题。该算法旨在计算相关松弛值函数重述的驻点，具体通过确定一系列代理问题的驻点序列来实现，其中代理问题对松弛值函数约束进行罚处理，上层和下层决策变量的更新是解耦的，且罚参数仅在某些迭代中增大——这些迭代未伴随某些可行性测度的充分改进。所提出的方法不包含任何线搜索，下层问题每次迭代仅需计算一次，且罚参数无需驱动至无穷大；尽管如此，在合理假设下仍获得了子序列收敛结果。数值实验中，松弛参数也被驱动至零，验证了该方法的有效性。
英文摘要
This paper is devoted to the introduction and analysis of a penalty-type method for the numerical treatment of a class of bilevel optimization problems arising from inverse optimal control. The algorithm is designed to compute stationary points of the associated relaxed value function reformulation. This is achieved by determining a sequence of stationary points associated with a sequence of surrogate problems where the relaxed value function constraint is penalized, where the updates of upper- and lower-level decision variables are decoupled, and where the penalty parameter is enlarged only in those iterations which do not come along with a sufficient improvement of some feasibility measure. The resulting method does not comprise any linesearch, the lower-level problem has to be evaluated just once per iteration, and the penalty parameter does not need to be driven to infinity. Nevertheless, subsequential convergence results are obtained under reasonable assumptions. Numerical experiments, where the relaxation parameter is also driven to zero, visualize effectiveness of the approach.
