A sequential solver for differential-algebraic equations with embedded optimization criteria (DAEOs) was developed to take advantage of the theoretical work done by Deussen et al. Solvers of this type separate the optimization problem from the differential equation and solve each individually. The new solver relies on the reduction of a DAEO to a sequence of differential inclusions separated by jump events. These jump events occur when the global solution to the optimization problem jumps to a new value. Without explicit treatment, these events will reduce the order of convergence of the integration step to one. The solver implements a "local optimizer tracking" procedure to detect and correct these jump events. Local optimizer tracking is much less expensive than running a deterministic global optimizer at every time step. This preserves the order of convergence of the integrator component without sacrificing performance to perform deterministic global optimization at every time step. The newly developed solver produces correct solutions to DAEOs and runs much faster than sequential DAEO solvers that rely only on global optimization.

翻译：本文开发了一种用于求解嵌入优化准则的微分代数方程（DAEOs）的序列求解器，以利用Deussen等人完成的理论工作。此类求解器将优化问题与微分方程分离并分别求解。新求解器依赖于将DAEO约化为由跳跃事件分隔的微分包含序列。当优化问题的全局解跳跃至新值时，这些跳跃事件就会发生。若不进行显式处理，这些事件将使积分步的收敛阶降至一阶。该求解器实现了"局部优化器追踪"程序来检测并修正这些跳跃事件。局部优化器追踪的计算成本远低于在每个时间步运行确定性全局优化器。这既保持了积分器组件的收敛阶数，又无需在每个时间步为执行确定性全局优化而牺牲性能。新开发的求解器能正确求解DAEOs，且运行速度远快于仅依赖全局优化的序列DAEO求解器。