A Greedy Newton-Type Method for Multiple Sparse Constraint Problem

Jun Sun (), Lingchen Kong () and Biao Qu ()
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Jun Sun: Linyi University
Lingchen Kong: Beijing Jiaotong University
Biao Qu: Qufu Normal University

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 3, No 3, 829-854

Abstract: Abstract With the development of science and technology, we can get many groups of data for the same object. There is a certain relationship with each other or structure between these data or within the data. To characterize the structure of the data in different datasets, in this paper, we propose a multiple sparse constraint problem (MSCP) to process the problem with multiblock sparse structure. We give three types of stationary points and present the relationships among the three types of stationary points and the global/local minimizers. Then we design a gradient projection Newton algorithm, which is proven to enjoy the global and quadratic convergence property. Finally, some numerical experiments of different examples illustrate the efficiency of the proposed method.

Keywords: Multiple sparse; Stationary point; Gradient projection Newton algorithm; Convergence analysis; Numerical experiment; 49M05; 90C26; 90C30; 65K05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-022-02156-2

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