Infeasibility Detection in the Alternating Direction Method of Multipliers for Convex Optimization
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10957_2019_1575_ReferencePDF.pdf
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Author(s)
Banjac, Goran
Goulart, Paul
Stellato, Bartolomeo
Boyd, Stephen
Date Issued
August 13, 2019
Publisher
Springer US
Version
Author's final manuscript
Abstract
Abstract
The alternating direction method of multipliers is a powerful operator splitting technique for solving structured optimization problems. For convex optimization problems, it is well known that the algorithm generates iterates that converge to a solution, provided that it exists. If a solution does not exist, then the iterates diverge. Nevertheless, we show that they yield conclusive information regarding problem infeasibility for optimization problems with linear or quadratic objective functions and conic constraints, which includes quadratic, second-order cone, and semidefinite programs. In particular, we show that in the limit the iterates either satisfy a set of first-order optimality conditions or produce a certificate of either primal or dual infeasibility. Based on these results, we propose termination criteria for detecting primal and dual infeasibility.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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DOI of Published Version
https://doi.org/10.1007/s10957-019-01575-y
