Abstract
Splitting algorithms for the sum of two monotone operators. We study two splitting algorithms for (stationary and evolution) problems involving the sum of two monotone operators. These algorithms are well known in the linear case and are here extended to the case of multivalued monotone operators. We prove the convergence of these algorithms, we give some applications to the obstacle problem and to minimization problems; and finally we present numerical computations comparing these algorithms to some other classical methods.
Keywords
Monotone polygonMathematicsAlgorithmConvergence (economics)Linear operatorsComputationOperator splittingNonlinear systemMinificationApplied mathematicsMathematical optimizationMathematical analysis
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Publication Info
- Year
- 1979
- Type
- article
- Volume
- 16
- Issue
- 6
- Pages
- 964-979
- Citations
- 1943
- Access
- Closed
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1943
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Cite This
Pierre‐Louis Lions,
Bertrand Mercier
(1979).
Splitting Algorithms for the Sum of Two Nonlinear Operators.
SIAM Journal on Numerical Analysis
, 16
(6)
, 964-979.
https://doi.org/10.1137/0716071
Identifiers
- DOI
- 10.1137/0716071