Accelerated Gradient and Skew-Symmetric Splitting Methods for a Class of Monotone Operator Equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916570107740160 |
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| author | Chen, Long Wei, Jingrong |
| author_facet | Chen, Long Wei, Jingrong |
| contents | A class of monotone operator equations, which can be decomposed into sum of the gradient of a strongly convex function and a linear and skew-symmetric operator, is considered in this work. Based on discretization of the generalized gradient flow, gradient and skew-symmetric splitting (GSS) methods are proposed and proved to converge in linear rates. To further accelerate the convergence, an accelerated gradient flow is proposed and accelerated gradient and skew-symmetric splitting (AGSS) methods are developed, which extends the acceleration among the existing works on the convex minimization to a more general class of monotone operator equations. In particular, when applied to smooth saddle point systems with bilinear coupling, a linear convergent method with optimal lower iteration complexity is proposed. The robustness and efficiency of GSS and AGSS methods are verified via extensive numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09009 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Accelerated Gradient and Skew-Symmetric Splitting Methods for a Class of Monotone Operator Equations Chen, Long Wei, Jingrong Optimization and Control 37N40 47H05 47J25 65B99 65J15 65L20 A class of monotone operator equations, which can be decomposed into sum of the gradient of a strongly convex function and a linear and skew-symmetric operator, is considered in this work. Based on discretization of the generalized gradient flow, gradient and skew-symmetric splitting (GSS) methods are proposed and proved to converge in linear rates. To further accelerate the convergence, an accelerated gradient flow is proposed and accelerated gradient and skew-symmetric splitting (AGSS) methods are developed, which extends the acceleration among the existing works on the convex minimization to a more general class of monotone operator equations. In particular, when applied to smooth saddle point systems with bilinear coupling, a linear convergent method with optimal lower iteration complexity is proposed. The robustness and efficiency of GSS and AGSS methods are verified via extensive numerical experiments. |
| title | Accelerated Gradient and Skew-Symmetric Splitting Methods for a Class of Monotone Operator Equations |
| topic | Optimization and Control 37N40 47H05 47J25 65B99 65J15 65L20 |
| url | https://arxiv.org/abs/2303.09009 |