@inproceedings{2d3e17ee209743f48882ac30ef939a4e,

title = "Gradient primal-dual algorithm converges to second-order stationary solution for nonconvex distributed optimization over networks",

abstract = "In this work, we study two first-order primal-dual based algorithms, the Gradient Primal-Dual Algorithm (GPDA) and the Gradient Alternating Direction Method of Multipliers (GADMM), for solving a class of linearly constrained non-convex optimization problems. We show that with random initialization of the primal and dual variables, both algorithms are able to compute second-order stationary solutions (ss2) with probability one. This is the first result showing that primal-dual algorithm is capable of finding ss2 when only using first-order information; it also extends the existing results for first-order, but primal-only algorithms. An important implication of our result is that it also gives rise to the first global convergence result to the ss2, for two classes of unconstrained distributed non-convex learning problems over multi-agent networks.",

author = "Mingyi Hong and Lee, {Jason D.} and Meisam Razaviyayn",

year = "2018",

month = jan,

day = "1",

language = "English (US)",

series = "35th International Conference on Machine Learning, ICML 2018",

publisher = "International Machine Learning Society (IMLS)",

pages = "3189--3198",

editor = "Jennifer Dy and Andreas Krause",

booktitle = "35th International Conference on Machine Learning, ICML 2018",

note = "35th International Conference on Machine Learning, ICML 2018 ; Conference date: 10-07-2018 Through 15-07-2018",

}