Abstract: Simultaneous solving principles of dynamic optimization problems based on differential-algebraic equations (DAE)were analyzed, and a concise description of the full discrete model based on Lobatto collocation was proposed. For the same original dynamic model, even though the number of discrete elements could be changed in each optimization process, the structures of the optimal solutions retained the similarity. A fast solving strategy of dynamic optimization, named self-heating approach, integrating the warm-start technology for the interior point method and the initial value setting method of barrier parameter, was proposed, and the novel solving approach used low-density discrete solution to approximate the high-density discrete solution. Finally, a test problem of crystallization process was solved by the proposed strategy, and the excellent results confirmed that the solving time could be cut to less than 1/6.

Key words: dynamic optimization, differential-algebraic equation, orthogonal collocation method

摘要： 分析了基于微分代数方程（DAE）的动态优化问题的联立求解原理，提出了基于Lobatto配置的全离散模型的简洁描述形式。根据离散化模型的最优解具有结构相似性的特点，利用低密度离散的解来近似高密度离散的解，并且配合内点法求解的暖启动技术与障碍参数初值设定方法，提出了能实现动态优化问题快速求解的自热式策略。最后通过求解一个结晶过程的动态优化算例，证实了所提出的自热式策略能够将求解速度提高6倍左右。

关键词: 动态优化, 代数微分方程, 正交配置法