An approximate ADMM for solving linearly constrained nonsmooth optimization problems with two blocks of variables
- Authors: Bagirov, Adil , Taheri, Sona , Bai, Fusheng , Wu, Zhiyou
- Date: 2019
- Type: Text , Book chapter
- Relation: Nonsmooth Optimization and Its Applications (part of the International Series of Numerical Mathematics book series) Chapter 2 p. 17-44
- Full Text: false
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- Description: Nonsmooth convex optimization problems with two blocks of variables subject to linear constraints are considered. A new version of the alternating direction method of multipliers is developed for solving these problems. In this method the subproblems are solved approximately. The convergence of the method is studied. New test problems are designed and used to verify the efficiency of the proposed method and to compare it with two versions of the proximal bundle method.
Discrete gradient methods
- Authors: Bagirov, Adil , Taheri, Sona , Karmitsa, Napsu
- Date: 2020
- Type: Text , Book chapter
- Relation: Numerical Nonsmooth Optimization: State of the Art Algorithms p. 621-654
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- Description: In this chapter, the notion of a discrete gradient is introduced and it is shown that the discrete gradients can be used to approximate subdifferentials of a broad class of nonsmooth functions. Two methods based on such approximations, more specifically, the discrete gradient method (DGM) and its limited memory version (LDGB), are described. These methods are semi derivative-free methods for solving nonsmooth and, in general, nonconvex optimization problems. The performance of the methods is demonstrated using some academic test problems. © Springer Nature Switzerland AG 2020.
Final words
- Authors: Bagirov, Adil , Gaudioso, Manlio , Karmitsa, Napsu , Mäkelä, Marko , Taheri, Sona
- Date: 2020
- Type: Text , Book chapter
- Relation: Numerical Nonsmooth Optimization: State of the Art Algorithms p. 693-694
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Introduction
- Authors: Bagirov, Adil , Gaudioso, Manlio , Karmitsa, Napsu , Mäkelä, Marko , Taheri, Sona
- Date: 2020
- Type: Text , Book chapter
- Relation: Numerical Nonsmooth Optimization: State of the Art Algorithms p. 1-16
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- Description: Nonsmooth optimization (NSO) is among the most challenging tasks in the field of mathematical programming. It addresses optimization problems where objective and/or constraint functions have discontinuous gradients. NSO problems arise in many real life applications. Moreover, some smooth optimization techniques like different decomposition methods, dual formulations and exact penalty methods may lead us to solve NSO problems being either smaller in dimension or simpler in structure. In addition, some optimization problems may be analytically smooth but numerically nonsmooth. This is the case, for instance, with noisy input data and so-called stiff problems, which are numerically unstable and behave like nonsmooth problems. © Springer Nature Switzerland AG 2020.
Limited Memory Bundle Method for Clusterwise Linear Regression
- Authors: Karmitsa, Napsu , Bagirov, Adil , Taheri, Sona , Joki, Kaisa
- Date: 2022
- Type: Text , Book chapter
- Relation: Intelligent Systems, Control and Automation: Science and Engineering p. 109-122
- Relation: http://purl.org/au-research/grants/arc/DP190100580
- Full Text: false
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- Description: A clusterwise linear regression problem consists of finding a number of linear functions each approximating a subset of the given data. In this paper, the limited memory bundle method is modified and combined with the incremental approach to solve this problem using its nonsmooth optimization formulation. The main contribution of the proposed method is to obtain a fast solution time for large-scale clusterwise linear regression problems. The proposed algorithm is tested on small and large real-world data sets and compared with other algorithms for clusterwise linear regression. Numerical results demonstrate that the proposed algorithm is especially efficient in data sets with large numbers of data points and input variables. © 2022, Springer Nature Switzerland AG.