  Homotopy optimization is a traditional method to deal with a complicated
optimization problem by solving a sequence of easy-to-hard surrogate
subproblems. However, this method can be very sensitive to the continuation
schedule design and might lead to a suboptimal solution to the original
problem. In addition, the intermediate solutions, often ignored by classic
homotopy optimization, could be useful for many real-world applications. In
this work, we propose a novel model-based approach to learn the whole
continuation path for homotopy optimization, which contains infinite
intermediate solutions for any surrogate subproblems. Rather than the classic
unidirectional easy-to-hard optimization, our method can simultaneously
optimize the original problem and all surrogate subproblems in a collaborative
manner. The proposed model also supports real-time generation of any
intermediate solution, which could be desirable for many applications.
Experimental studies on different problems show that our proposed method can
significantly improve the performance of homotopy optimization and provide
extra helpful information to support better decision-making.
