期刊
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
卷 73, 期 1, 页码 201-235出版社
SPRINGER
DOI: 10.1007/s10589-019-00072-2
关键词
Separable convex optimization; Alternating direction method of multipliers; Multiple blocks; Inexact ADMM; Global convergence
资金
- National Science Foundation [1522629, 1522654, 1819002, 1819161]
- Office of Naval Research [N00014-15-1-2048, N00014-18-1-2100]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1522629, 1522654] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1819002, 1819161] Funding Source: National Science Foundation
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach involves linearized subproblems, a back substitution step, and either gradient or accelerated gradient techniques. Global convergence is established. The methods are particularly useful when the ADMM subproblems do not have closed form solution or when the solution of the subproblems is expensive. Numerical experiments based on image reconstruction problems show the effectiveness of the proposed methods.
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