We study the set of continuous functions that admit no spurious local optima (i.e.

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).

We study the set of continuous functions that admit no spurious local optima (i.e. They satisfy various powerful properties for analyzing nonconvex and nonsmooth optimization problems. For instance, they satisfy a theorem akin to the fundamental uniform limit theorem in the analysis regarding continuous functions. Global functions are also endowed with useful properties regarding the composition of functions and change of variables. Using these new results, we show that a class of non-differentiable nonconvex optimization problems arising in tensor decomposition applications are global functions.