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Deriving Solution Value Bounds from the ADMM

Jonathan Eckstein (jeckstei***at***business.rutgers.edu)

Abstract: This short paper describes a simple subgradient-based techniques for deriving bounds on the optimal solution value when using the ADMM to solve convex optimization problems. The technique requires a bound on the magnitude of some optimal solution vector, but is otherwise completely general. Some computational examples using LASSO problems demonstrate that the technique can produce steadily converging bounds in situations in which standard Lagrangian bounds yield little or no useful information.

Keywords: ADMM, convex optimization

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 11/23/2019
Entry Accepted: 11/23/2019
Entry Last Modified: 11/23/2019

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