An Inexact Projected Gradient Method for Sparsity-Constrained Quadratic Measurements Regression

Jun Fan, Liqun Wang () and Ailing Yan ()
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Jun Fan: Institute of Mathematics, Hebei University of Technology, Tianjin 300401, P. R. China
Liqun Wang: Department of Statistics, University of Manitoba, Winnipeg, R3T 2N2, Canada
Ailing Yan: Institute of Mathematics, Hebei University of Technology, Tianjin 300401, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2019, vol. 36, issue 02, 1-21

Abstract: In this paper, we employ the sparsity-constrained least squares method to reconstruct sparse signals from the noisy measurements in high-dimensional case, and derive the existence of the optimal solution under certain conditions. We propose an inexact sparse-projected gradient method for numerical computation and discuss its convergence. Moreover, we present numerical results to demonstrate the efficiency of the proposed method.

Keywords: Quadratic measurements regression; sparsity; uniform s-regularity; uniqueness; greedy algorithm (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0217595919400086

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