| 両方とも前のリビジョン 前のリビジョン 次のリビジョン | 前のリビジョン 次のリビジョン両方とも次のリビジョン |
| en:intro:researches:optimization [2019/12/17 10:18] – [Decentralized Optimization Algorithms] Hideaki IIDUKA | en:intro:researches:optimization [2020/02/21 10:49] – [Decentralized Optimization Algorithms] Hideaki IIDUKA |
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| Here, we divide the problem into the three categories. | Here, we divide the problem into the three categories. |
| - **Smooth Convex Optimization Problem**:\\ It assumes that $f^{(i)}$ $(i\in \mathcal{I})$ is smooth and convex. The problem includes [[http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1206687&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F78%2F27152%2F01206687.pdf%3Farnumber%3D1206687|signal recovery problem]], [[http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4291862&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F78%2F4291841%2F04291862.pdf%3Farnumber%3D4291862|beamforming problem]], [[http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4604754&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F49%2F4604726%2F04604754.pdf%3Farnumber%3D4604754|storage allocation problem]], [[http://epubs.siam.org/doi/abs/10.1137/110850542|optimal control problem]], and [[http://epubs.siam.org/doi/abs/10.1137/120866877|bandwidth allocation problem]]. | - **Smooth Convex Optimization Problem**:\\ It assumes that $f^{(i)}$ $(i\in \mathcal{I})$ is smooth and convex. The problem includes [[http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1206687&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F78%2F27152%2F01206687.pdf%3Farnumber%3D1206687|signal recovery problem]], [[http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4291862&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F78%2F4291841%2F04291862.pdf%3Farnumber%3D4291862|beamforming problem]], [[http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4604754&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F49%2F4604726%2F04604754.pdf%3Farnumber%3D4604754|storage allocation problem]], [[http://epubs.siam.org/doi/abs/10.1137/110850542|optimal control problem]], and [[http://epubs.siam.org/doi/abs/10.1137/120866877|bandwidth allocation problem]]. |
| - **Nonsmooth Convex Optimization Problem**:\\ It assumes that $f^{(i)}$ $(i\in \mathcal{I})$ is nonsmooth and convex. The problem includes [[http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4407760&filter%3DAND%28p_IS_Number%3A4407756%29|signal recovery problem]],[[http://www.sciencedirect.com/science/article/pii/S0925231214000964|ensemble learning]], [[http://link.springer.com/chapter/10.1007/978-1-4419-9569-8_17|minimal antenna-subset selection problem]], and [[https://ieeexplore.ieee.org/document/8584116|bandwidth allocation problem]]. | - **Nonsmooth Convex Optimization Problem**:\\ It assumes that $f^{(i)}$ $(i\in \mathcal{I})$ is nonsmooth and convex. The problem includes [[http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4407760&filter%3DAND%28p_IS_Number%3A4407756%29|signal recovery problem]],[[https://ieeexplore.ieee.org/document/8744480|ensemble learning]], [[http://link.springer.com/chapter/10.1007/978-1-4419-9569-8_17|minimal antenna-subset selection problem]], and [[https://ieeexplore.ieee.org/document/8584116|bandwidth allocation problem]]. |
| - **Smooth Nonconvex Optimization Problem**\\ It assumes that $f^{(i)}$ $(i\in \mathcal{I})$ is smooth and nonconvex. The problem has practical problems such as [[http://link.springer.com/article/10.1007%2Fs10107-010-0427-x#|power control]] and [[http://epubs.siam.org/doi/abs/10.1137/110849456|bandwidth allocation]]. | - **Smooth Nonconvex Optimization Problem**\\ It assumes that $f^{(i)}$ $(i\in \mathcal{I})$ is smooth and nonconvex. The problem has practical problems such as [[http://link.springer.com/article/10.1007%2Fs10107-010-0427-x#|power control]] and [[http://epubs.siam.org/doi/abs/10.1137/110849456|bandwidth allocation]]. |
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| ==== Decentralized Optimization Algorithms ==== | ==== Decentralized Optimization Algorithms ==== |
| [[http://epubs.siam.org/doi/abs/10.1137/S1052623499362111|The incremental subgradient method]] and [[http://iopscience.iop.org/0266-5611/24/6/065014|the broadcast optimization method]] are useful for decentralized convex optimization. However, they can be applied to only the case where $C^{(i)} = C$ $(i\in \mathcal{I})$ and $C$ is simple in the sense that the projection onto $C$ can be easily computed (e.g., $C$ is a half-space). We have proposed decentralized optimization algorithms for solving convex optimization problems with more complicated $C^{(i)}$ (e.g., $C^{(i)}$ is the intersection of simple, closed convex sets), which include [[http://epubs.siam.org/doi/abs/10.1137/120866877|bandwidth allocation problem]] and [[http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4604754&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F49%2F4604726%2F04604754.pdf%3Farnumber%3D4604754|storage allocation problem]]. | [[http://epubs.siam.org/doi/abs/10.1137/S1052623499362111|The incremental subgradient method]] and [[http://iopscience.iop.org/0266-5611/24/6/065014|the broadcast optimization method]] are useful for decentralized convex optimization. However, they can be applied to only the case where $C^{(i)} = C$ $(i\in \mathcal{I})$ and $C$ is simple in the sense that the projection onto $C$ can be easily computed (e.g., $C$ is a half-space). We have proposed decentralized optimization algorithms for solving convex optimization problems with more complicated $C^{(i)}$ (e.g., $C^{(i)}$ is the intersection of simple, closed convex sets), which include [[http://epubs.siam.org/doi/abs/10.1137/120866877|bandwidth allocation problem]], [[http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4604754&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F49%2F4604726%2F04604754.pdf%3Farnumber%3D4604754|storage allocation problem]], and [[https://ieeexplore.ieee.org/document/8744480|ensemble learning]]. |
| * [[:en:iiduka:|H. Iiduka]]: [[https://ieeexplore.ieee.org/document/8744480|Stochastic Fixed Point Optimization Algorithm for Classifier Ensemble]], IEEE Transactions on Cybernetics (accepted) | * [[:en:iiduka:|H. Iiduka]]: [[https://ieeexplore.ieee.org/document/8744480|Stochastic Fixed Point Optimization Algorithm for Classifier Ensemble]], IEEE Transactions on Cybernetics (accepted) |
| * [[:en:iiduka:|H. Iiduka]]: [[https://link.springer.com/article/10.1007/s11081-019-09440-7|Decentralized Hierarchical Constrained Convex Optimization]], Optimization and Engineering (accepted) | * [[:en:iiduka:|H. Iiduka]]: [[https://link.springer.com/article/10.1007/s11081-019-09440-7|Decentralized Hierarchical Constrained Convex Optimization]], Optimization and Engineering (accepted) |