Complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs

Abstract

This paper analyzes the iteration-complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs. More specifically, the objective function is of the form $f+h$ where $f$ is a differentiable function whose gradient is Lipschitz continuous and $h$ is a closed convex function with bounded domain. The method, basically, consists of applying an accelerated inexact proximal point method for solving approximately a sequence of quadratic penalized subproblems associated to the linearly constrained problem. Each subproblem of the proximal point method is in turn approximately solved by an accelerated composite gradient (ACG) method. It is shown that the proposed scheme generates a $\rho$-approximate stationary point in at most $\mathcal{O}({\rho }^{-3})$ ACG iterations. Finally, numerical results showing the efficiency of the proposed method are also given.

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Cited by in corpus (5)

• A Doubly Accelerated Inexact Proximal Point Method for Nonconvex Composite Optimization Problems
• A Proximal Alternating Direction Method of Multiplier for Linearly Constrained Nonconvex Minimization
• Accelerated Stochastic Algorithms for Nonconvex Finite-sum and Multi-block Optimization
• Efficiency of Coordinate Descent Methods For Structured Nonconvex Optimization
• Decentralized Non-Convex Learning with Linearly Coupled Constraints