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We develop a unified level-bundle method, called accelerated constrained level-bundle (ACLB) algorithm, for solving constrained convex optimization problems. where the objective and constraint functions can be nonsmooth, weakly smooth, and/or smooth. ACLB employs Nesterov’s accelerated gradient technique, and hence retains the iteration complexity as that of existing bundle-type methods if the objective or one of the constraint functions is nonsmooth. More importantly, ACLB can significantly reduce iteration complexity when the objective and all constraints are (weakly) smooth. In addition, if the objective contains a nonsmooth component which can be written as a specific form of maximum, we show that the iteration complexity of this component can be much lower than that for general nonsmooth objective function. Numerical results demonstrate the effectiveness of the proposed algorithm.
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Fully Proximal Splitting Algorithms In Image Recovery
Structured convex optimization problems in image recovery typically involve a mix of smooth and nonsmooth functions. The common practice is to activate the smooth functions via their gradient and the nonsmooth ones via their proximity operator. We show that, although intuitively natural, this approach is not necessarily the most efficient numerically and that, in particular, activating all the functions proximally may be advantageous. To make this viewpoint viable computationally, we derive a number of new examples of proximity operators of smooth convex functions arising in applications.
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- Award ID(s):
- 1715671
- PAR ID:
- 10163516
- Date Published:
- Journal Name:
- 27th European Signal Processing Conference (EUSIPCO)
- Volume:
- 2019
- Page Range / eLocation ID:
- 1 to 5
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We develop a unified level-bundle method, called accelerated constrained level-bundle (ACLB) algorithm, for solving constrained convex optimization problems. where the objective and constraint functions can be nonsmooth, weakly smooth, and/or smooth. ACLB employs Nesterov’s accelerated gradient technique, and hence retains the iteration complexity as that of existing bundle-type methods if the objective or one of the constraint functions is nonsmooth. More importantly, ACLB can significantly reduce iteration complexity when the objective and all constraints are (weakly) smooth. In addition, if the objective contains a nonsmooth component which can be written as a specific form of maximum, we show that the iteration complexity of this component can be much lower than that for general nonsmooth objective function. Numerical results demonstrate the effectiveness of the proposed algorithm.more » « less
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/EUSIPCO.2019.8903039
