This paper shows how bounds on subproblem objective value suboptimality can be used in inexact augmented Lagrangian methods and ADMM algorithms, and enables two new approaches to computing Lagrangian bounds on the optimal values of stochastic mixed-integer programming problems.
Abstract
Through a"partial strong convexity"lemma, this paper shows how bounds on subproblem objective value suboptimality can be used in inexact augmented Lagrangian methods and ADMM algorithms. The ADMM result uses a small but important refinement on a long-standing criterion for approximately solving subproblems. The results enable two new approaches to computing Lagrangian bounds on the optimal values of stochastic mixed-integer programming problems, with simpler convergence analysis than the prior state of the art. In each case, the subproblems are solved by variants of the classical Frank-Wolfe algorithm. However, as compared to prior methods of the same type, there is much more freedom in the choice of Frank-Wolfe variant.
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