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Iteration-complexity of a Rockafellar's proximal method of multipliers for convex programming based on second-order approximations

Maicon M. Alves(maicon.alves***at***ufsc.br)
R. D. C. Monteiro(monteiro***at***isye.gatech.edu)
Benar F. Svaiter(benar***at***impa.br)

Abstract: This paper studies the iteration-complexity of a new primal-dual algorithm based on Rockafellar's proximal method of multipliers (PMM) for solving smooth convex programming problems with inequality constraints. In each step, either a step of Rockafellar's PMM for a second-order model of the problem is computed or a relaxed extragradient step is performed. The resulting algorithm is a (large-step) relaxed hybrid proximal extragradient (r-HPE) method of multipliers, which combines Rockafellar's PMM with the r-HPE method.

Keywords: convex programming, proximal method of multipliers, second-order methods, hybrid extragradient, complexity

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Global Optimization


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Entry Submitted: 02/21/2016
Entry Accepted: 02/21/2016
Entry Last Modified: 02/21/2016

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