Split Bregman iteration for multi-period mean variance portfolio optimization

Corsaro, Stefania; Simone, Valentina De; Marino, Zelda

doi:10.1016/j.amc.2020.125715

Cited by 21 publications

(16 citation statements)

References 31 publications

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“…Split Bregman iteration can transform a difficult optimization problem into several simple subproblems. Then the subproblems are solved and updated alternately [26][27][28]. Based on the methodology of split Bregman iteration, we introduce…”

Section: Solvution Algorithm Using Acceleration Schemementioning

confidence: 99%

Fast Terahertz Imaging Model Based on Group Sparsity and Nonlocal Self-Similarity

et al. 2022

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In order to solve the problems of long-term image acquisition time and massive data processing in a terahertz time domain spectroscopy imaging system, a novel fast terahertz imaging model, combined with group sparsity and nonlocal self-similarity (GSNS), is proposed in this paper. In GSNS, the structure similarity and sparsity of image patches in both two-dimensional and three-dimensional space are utilized to obtain high-quality terahertz images. It has the advantages of detail clarity and edge preservation. Furthermore, to overcome the high computational costs of matrix inversion in traditional split Bregman iteration, an acceleration scheme based on conjugate gradient method is proposed to solve the terahertz imaging model more efficiently. Experiments results demonstrate that the proposed approach can lead to better terahertz image reconstruction performance at low sampling rates.

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Section: Solvution Algorithm Using Acceleration Schemementioning

confidence: 99%

Fast Terahertz Imaging Model Based on Group Sparsity and Nonlocal Self-Similarity

et al. 2022

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“…Computational Experience. We test the effectiveness of the IP-PMM applied to the fused lasso model on the following real-world data sets: [19,20], we generate 10 problems with annual or quarterly rebalancing, after a preprocessing procedure that eliminates the elements with the highest volatilities. A rolling window (RW) for setting up the model parameters is considered.…”

Section: Portfolio Selection Problemmentioning

confidence: 99%

Sparse Approximations with Interior Point Methods

Simone¹,

Serafino²,

Gondzio³

et al. 2021

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Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience on a variety of problems, namely, multi-period portfolio optimization, classification of data coming from functional Magnetic Resonance Imaging, restoration of images corrupted by Poisson noise, and classification via regularized logistic regression, provides substantial evidence that interior point methods, equipped with suitable linear algebra, can offer a noticeable advantage over first-order approaches.

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“…The basic idea of the split Bregman iteration is that a complex optimization problem can be split into a few unconstrained subproblems by introducing the variable splitting technique. Experimental results show that the algorithm has a fast convergence speed and small memory occupation, which is very attractive for large-scale optimization problems [26][27][28]. Based on a split Bregman iteration algorithmic framework, we first transform the optimization problem (11) (12) where  and  are regularization parameters.…”

Section: For a Given Sample Imagementioning

confidence: 99%

Hybrid Sparsity Model for Fast Terahertz Imaging

2021

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In order to shorten the long-term image acquisition time of the terahertz time domain spectroscopy imaging system while ensuring the imaging quality, a hybrid sparsity model (HSM) is proposed for fast terahertz imaging in this paper, which incorporates both intrinsic sparsity prior and nonlocal self-similarity constraints in a unified statistical model. In HSM, a weighted exponentiation shift-invariant wavelet transform is introduced to enhance the sparsity of the terahertz image. Simultaneously, the nonlocal self-similarity by means of the three-dimensional sparsity in the transform domain is exploited to ensure high-quality terahertz image reconstruction. Finally, a new split Bregman-based iteration algorithm is developed to solve the terahertz imaging model more efficiently. Experiments are presented to verify the effectiveness of the proposed approach.

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Split Bregman iteration for multi-period mean variance portfolio optimization

Abstract: Highlights A point-to-point response to reviewers’ comments is given in the response letter to them. In the submitted revision all changes are highlighted in blue.

Cited by 21 publications

References 31 publications

Fast Terahertz Imaging Model Based on Group Sparsity and Nonlocal Self-Similarity

Fast Terahertz Imaging Model Based on Group Sparsity and Nonlocal Self-Similarity

Sparse Approximations with Interior Point Methods

Hybrid Sparsity Model for Fast Terahertz Imaging

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