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.