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Iteration-complexity of a Jacobi-type non-Euclidean ADMM for multi-block linearly constrained nonconvex programs

Jefferson Melo(jefferson***at***ufg.br)
Renato Monteiro(monteiro***at***isye.gatech.edu)

Abstract: This paper establishes the iteration-complexity of a Jacobi-type non-Euclidean proximal alternating direction method of multipliers (ADMM) for solving multi-block linearly constrained nonconvex programs. The subproblems of this ADMM variant can be solved in parallel and hence the method has great potential to solve large scale multi-block linearly constrained nonconvex programs. Moreover, our analysis allows the Lagrange multiplier to be updated with a relaxation parameter in the interval (0, 2).

Keywords: Jacobi multiblock ADMM, nonconvex program, iteration-complexity, first-order methods, non-Euclidean distances.

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 05/19/2017
Entry Accepted: 05/19/2017
Entry Last Modified: 05/19/2017

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