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The rate of convergence of proximal method of multipliers for second-order cone optimization problems

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Abstract

In this paper we consider a proximal method of multipliers (PMM) for a nonlinear second-order cone optimization problem. With the assumptions of constraint nondegeneracy, strict complementarity and second-order sufficient condition, we estimate the local convergence rate of PMM to be linear or superlinear, which depends on the strategy of parameter selection.

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Acknowledgements

Bo Wang: Research is supported in part by the National Natural Science Foundation of China under Project No. 11701091. Li-Wei Zhang: Research was supported by the National Natural Science Foundation of China (11971089, 11571059 and 11731013).

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Li Chu

  2. City Institute, Dalian University of Technology, Dalian, 116600, China

    Li Chu

  3. Key Laboratory of Operations Research and Control of Universities in Fujian, College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350116, China

    Bo Wang

  4. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Liwei Zhang & Hongwei Zhang

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  1. Li Chu
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  2. Bo Wang
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  3. Liwei Zhang
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  4. Hongwei Zhang
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Correspondence to Bo Wang.

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Chu, L., Wang, B., Zhang, L. et al. The rate of convergence of proximal method of multipliers for second-order cone optimization problems. Optim Lett 15, 441–457 (2021). https://doi.org/10.1007/s11590-020-01607-x

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  • DOI: https://doi.org/10.1007/s11590-020-01607-x

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