Non-convex regularization and accelerated gradient algorithm for sparse portfolio selection

In portfolio optimization, non-convex regularization has recently been recognized as an important approach to promote sparsity, while countervailing the shortcomings of convex penalty. In this paper, we customize the non-convex piecewise quadratic approximation (PQA) function considering the backgro...

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Bibliographic Details
Published in:Optimization methods & software Vol. 38; no. 2; pp. 434 - 456
Main Authors: Li, Qian, Zhang, Wei, Wang, Guoqiang, Bai, Yanqin
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.03.2023
Taylor & Francis Ltd
Subjects:
accelerated proximal algorithm
Algorithms
Empirical analysis
linear convergence
Mathematical models
non-convex regularization
Optimization
Parameters
Portfolio management
Regularization
Sharpe ratio
Sparse portfolio selection
Sparsity
turnover
ISSN:1055-6788, 1029-4937
Online Access:Get full text
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Summary:In portfolio optimization, non-convex regularization has recently been recognized as an important approach to promote sparsity, while countervailing the shortcomings of convex penalty. In this paper, we customize the non-convex piecewise quadratic approximation (PQA) function considering the background of portfolio management and present the PQA regularized mean-variance model (PMV). By exposing the feature of PMV, we prove that a KKT point of PMV is a local minimizer if the regularization parameter satisfies a mild condition. Besides, the theoretical sparsity of PMV is analysed, which is associated with the regularization parameter and the weight parameter. To solve this model, we introduce the accelerated proximal gradient (APG) algorithm, whose improved linear convergence rate compared with proximal gradient (PG) algorithm is developed. Moreover, the optimal accelerated parameter of APG algorithm for PMV is attained. These theoretical results are further illustrated with numerical experiments. Finally, empirical analysis demonstrates that the proposed model has a better out-of-sample performance and a lower turnover than many other existing models on the tested datasets.
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ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2022.2142580