Reviews: A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization

This paper studies the condition for absence of spurious optimality. In particular, the authors introduce'global functions' to define the set of continuous functions that admit no spurious local optima (in the sense of sets), and develop some corresponding definitions and propositions for an extending characterization of continuous functions that admit no spurious strict local optima. The authors also apply their theory to l1-norm minimization in tensor decomposition. Pros: In my opinion, the main contribution of this paper is to establish a general math result and apply it to study the absence of spurious optimality for a specific problem. I also find some mathematical discoveries on global functions interesting, which include: -- In section 2, the paper provides two examples to show that: (i).