Majorized iPADMM for Nonseparable Convex Minimization Models with Quadratic Coupling Terms

Yumin Ma (), Ting Li (), Yongzhong Song () and Xingju Cai
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Yumin Ma: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023 P. R. China
Ting Li: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023 P. R. China
Yongzhong Song: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023 P. R. China
Xingju Cai: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023 P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2023, vol. 40, issue 01, 1-35

Abstract: In this paper, we consider nonseparable convex minimization models with quadratic coupling terms arised in many practical applications. We use a majorized indefinite proximal alternating direction method of multipliers (iPADMM) to solve this model. The indefiniteness of proximal matrices allows the function we actually solved to be no longer the majorization of the original function in each subproblem. While the convergence still can be guaranteed and larger stepsize is permitted which can speed up convergence. For this model, we analyze the global convergence of majorized iPADMM with two different techniques and the sublinear convergence rate in the nonergodic sense. Numerical experiments illustrate the advantages of the indefinite proximal matrices over the positive definite or the semi-definite proximal matrices.

Keywords: Nonseparable convex minimization model; majorized iPADMM; indefinite proximal terms; quadratic coupling terms; convergence (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0217595922400024

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