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Convergence analysis of a nonmonotone projected gradient method for multiobjective optimization problems

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Abstract

In this work we consider an extension of the projected gradient method (PGM) to constrained multiobjective problems. The projected gradient scheme for multiobjective optimization proposed by Graña Drummond and Iusem and analyzed by Fukuda and Graña Drummond is extended to include a nonmonotone line search based on the average of the successive previous functions values instead of the traditional Armijo-like rules. Under standard assumptions, stationarity of the accumulation points is established. Moreover, under standard convexity assumptions, we prove full convergence to weakly Pareto optimal solutions of any sequence produced by the proposed algorithm.

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Acknowledgements

The authors are indebted to the anonymous referees whose comments helped a lot to improve the quality of the paper.

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Authors and Affiliations

  1. CONICET, Department of Mathematics, FCE, University of La Plata, La Plata, Argentina

    N. S. Fazzio & M. L. Schuverdt

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  1. N. S. Fazzio
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  2. M. L. Schuverdt
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Correspondence to M. L. Schuverdt.

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Fazzio, N.S., Schuverdt, M.L. Convergence analysis of a nonmonotone projected gradient method for multiobjective optimization problems. Optim Lett 13, 1365–1379 (2019). https://doi.org/10.1007/s11590-018-1353-8

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  • DOI: https://doi.org/10.1007/s11590-018-1353-8

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