Contractive Difference-of-Convex Algorithms

Songnian He (), Qiao-Li Dong () and Michael Th. Rassias ()
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Songnian He: Civil Aviation University of China
Qiao-Li Dong: Civil Aviation University of China
Michael Th. Rassias: Hellenic Military Academy

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 1, No 12, 21 pages

Abstract: Abstract The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be solved by iterative methods such as proximal gradient algorithm. However, these algorithms essentially belong to some iterative methods of fixed point problems of averaged mappings, and their convergence speed is generally slow. Furthermore, there is seldom research on the termination rule of these iterative algorithms solving the subproblem of DCA. To overcome these defects, we firstly show that the subproblem of the linearized proximal method (LPM) in each iteration is equal to the fixed point problem of a contraction. Secondly, by using Picard iteration to approximately solve the subproblem of LPM in each iteration, we propose a contractive difference-of-convex algorithm (cDCA) where an adaptive termination rule is presented. Both global subsequential convergence and global convergence of the whole sequence of cDCA are established. Finally, preliminary results from numerical experiments are promising.

Keywords: Linearized proximal method; Contractive difference-of-convex algorithm; Kurdyka–Łojasiewicz property; Difference-of-convex optimization problem.; 90C30; 65K05; 90C26 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02689-2

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