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A proximal bundle-based algorithm for nonsmooth constrained multiobjective optimization problems with inexact data

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Abstract

In this paper, a proximal bundle-based method for solving nonsmooth nonconvex constrained multiobjective optimization problems with inexact information is proposed and analyzed. In this method, each objective function is treated individually without employing any scalarization. Using the improvement function, we transform the problem into an unconstrained one. At each iteration, by the proximal bundle method, a piecewise linear model is built and by solving a convex subproblem, a new candidate iterate is obtained. For locally Lipschitz objective and constraint functions, we study the problem of computing an approximate substationary point (a substationary point), when only inexact (exact) information about the functions and subgradient values are accessible. At the end, some numerical experiments are provided to illustrate the effectiveness of the method and certify the theoretical results.

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Acknowledgements

The first-named author is grateful to National Elite Foundation of Iran for its financial support. The authors would like to thank two anonymous referees for their comments that helped to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran

    N. Hoseini Monjezi & S. Nobakhtian

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  1. N. Hoseini Monjezi
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  2. S. Nobakhtian
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Correspondence to S. Nobakhtian.

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Hoseini Monjezi, N., Nobakhtian, S. A proximal bundle-based algorithm for nonsmooth constrained multiobjective optimization problems with inexact data. Numer Algor 89, 637–674 (2022). https://doi.org/10.1007/s11075-021-01128-3

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  • DOI: https://doi.org/10.1007/s11075-021-01128-3

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