A Stochastic Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization
نویسندگان
چکیده
where (a) because that E and Tr are both linear operators and Tr[E[ZZ ]] is certain positive number which is independent on the optimization variables, then this term can be replaced by another positive constant Tr[EZ[Z ]EZ[Z]]. Based on the equivalence between (13) and (14), we can apply the result shown in [28, Lemma 2]. Since the constraint set is polyhedral in the formulation (3), the linear constraint qualification (LCQ) condition is satisfied. Therefore, a Karush-Kuhn-Tucker (KKT) point always exists, and it corresponds to the points that satisfy the first-order stationary solution. Then, the claim is true.
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