On the Behavior of the Douglas--Rachford Algorithm for Minimizing a Convex Function Subject to a Linear Constraint
| Autor: | Walaa M. Moursi, Heinz H. Bauschke |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
021103 operations research
0211 other engineering and technologies Regular polygon 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Theoretical Computer Science Constraint (information theory) Optimization and Control (math.OC) 49M27 65K10 90C25 47H14 49M29 Subject (grammar) FOS: Mathematics 0101 mathematics Convex function Mathematics - Optimization and Control Algorithm Software Mathematics |
| Zdroj: | SIAM Journal on Optimization. 30:2559-2576 |
| ISSN: | 1095-7189 1052-6234 |
| Popis: | The Douglas-Rachford algorithm (DRA) is a powerful optimization method for minimizing the sum of two convex (not necessarily smooth) functions. The vast majority of previous research dealt with the case when the sum has at least one minimizer. In the absence of minimizers, it was recently shown that for the case of two indicator functions, the DRA converges to a best approximation solution. In this paper, we present a new convergence result on the the DRA applied to the problem of minimizing a convex function subject to a linear constraint. Indeed, a normal solution may be found even when the domain of the objective function and the linear subspace constraint have no point in common. As an important application, a new parallel splitting result is provided. We also illustrate our results through various examples. |
| Databáze: | OpenAIRE |
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