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Yue Xie (xie86wisc.edu) Abstract: We analyze worstcase complexity of a proximal augmented Lagrangian (proximal AL) framework for nonconvex optimization with nonlinear equality constraints. When a firstorder (secondorder) optimal point is obtained in the subproblem, an $\epsilon$ firstorder (secondorder) optimal point for the original problem can be guaranteed within $\mathcal{O}(1/ \epsilon^{2  \eta})$ outer iterations (where $\eta$ is a userdefined parameter with $\eta\in[0,2]$ for the firstorder result and $\eta \in [1,2]$ for the secondorder result) when the proximal term coefficient $\beta$ and penalty parameter $\rho$ satisfy $\beta = \mathcal{O}(\epsilon^\eta)$ and $\rho = \mathcal{O}(1/\epsilon^\eta)$, respectively. Further, when the subproblems are solved inexactly, the same order of complexity can be recovered by imposing certain verifiable conditions on the error sequence. We also investigate the total iteration complexity and operation complexity when a Newtonconjugategradient algorithm is used to solve the subproblems. Keywords: Nonconvex optimization with nonlinear equality constraints; Proximal augmented Lagrangian; Complexity analysis; Newtonconjugategradient Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Download: [PDF] Entry Submitted: 07/31/2019 Modify/Update this entry  
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