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Majorized iPADMM for Nonseparable Convex Minimization Models with Quadratic Coupling Terms

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yumin Ma & Ting Li & Yongzhong Song & Xingju Cai, 2023. "Majorized iPADMM for Nonseparable Convex Minimization Models with Quadratic Coupling Terms," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(01), pages 1-35, February.
    • Handle: RePEc:wsi:apjorx:v:40:y:2023:i:01:n:s0217595922400024
    DOI: 10.1142/S0217595922400024
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