Convergence Analysis of the Generalized Splitting Methods for a Class of Nonconvex Optimization Problems

Min Li () and Zhongming Wu ()
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Min Li: Nanjing University
Zhongming Wu: Southeast University

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 2, No 8, 535-565

Abstract: Abstract In this paper, we propose generalized splitting methods for solving a class of nonconvex optimization problems. The new methods are extended from the classic Douglas–Rachford and Peaceman–Rachford splitting methods. The range of the new step-sizes even can be enlarged two times for some special cases. The new methods can also be used to solve convex optimization problems. In particular, for convex problems, we propose more relax conditions on step-sizes and other parameters and prove the global convergence and iteration complexity without any additional assumptions. Under the strong convexity assumption on the objective function, the linear convergence rate can be derived easily.

Keywords: Competing structure; Lipschitz continuous; Nonconvex optimization problems; Splitting methods; Step-size; 90C25; 90C33; 65K05 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-019-01564-1

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