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Error bound analysis, which estimates the distance of a point to the solutionset of an optimization problem using the optimality residual, is a powerfultool for the analysis of first-order optimization algorithms. In this paper, weuse global error bound analysis to study the iteration complexity of afirst-order algorithm for a linearly constrained nonconvex minimizationproblem. we develop a global dual error bound analysis for a regularizedversion of this nonconvex problem by using a novel ``decomposition'' technique.Equipped with this global dual error bound, we prove that a suitably designedprimal-dual first order method can generate an $\epsilon$-stationary solutionof the linearly constrained nonconvex minimization problem within$\mathcal{O}(1/\epsilon^2)$ iterations, which is the best known iterationcomplexity for this class of nonconvex problems.

A global dual error bound and its application to the analysis of linearly constrained nonconvex optimization