Douglas–Rachford Splitting for the Sum of a Lipschitz Continuous and a Strongly Monotone Operator
Autor: | Lieven Vandenberghe, Walaa M. Moursi |
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Rok vydání: | 2019 |
Předmět: |
TheoryofComputation_MISCELLANEOUS
021103 operations research Control and Optimization Applied Mathematics Mathematics::Optimization and Control 0211 other engineering and technologies Monotonic function 010103 numerical & computational mathematics 02 engineering and technology Subderivative Management Science and Operations Research Lipschitz continuity Strongly monotone 01 natural sciences Operator (computer programming) Monotone polygon Rate of convergence Applied mathematics 0101 mathematics Convex function Mathematics |
Zdroj: | Journal of Optimization Theory and Applications. 183:179-198 |
ISSN: | 1573-2878 0022-3239 |
Popis: | The Douglas–Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper, closed, and convex functions and, more generally, two maximally monotone operators. Recent results concerned with linear rates of convergence of the method require additional properties of the underlying monotone operators, such as strong monotonicity and cocoercivity. In this paper, we study the case, when one operator is Lipschitz continuous but not necessarily a subdifferential operator and the other operator is strongly monotone. This situation arises in optimization methods based on primal–dual approaches. We provide new linear convergence results in this setting. |
Databáze: | OpenAIRE |
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