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An inexact scalarization proximal point method for multiobjective quasiconvex minimization

Author

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  • E. A. Papa Quiroz

    (Privada del Norte University and Mayor de San Marcos National University)

  • S. Cruzado

    (Mayor de San Marcos National University)

Abstract

In this paper we present an inexact scalarization proximal point algorithm to solve unconstrained multiobjective minimization problems where the objective functions are quasiconvex and locally Lipschitz. Under some natural assumptions on the problem, we prove that the sequence generated by the algorithm is well defined and converges. Then providing two error criteria we obtain two versions of the algorithm and it is proved that each sequence converges to a Pareto–Clarke critical point of the problem; furthermore, it is also proved that assuming an extra condition, the convergence rate of one of these versions is linear when the regularization parameters are bounded and superlinear when these parameters converge to zero.

Suggested Citation

  • E. A. Papa Quiroz & S. Cruzado, 2022. "An inexact scalarization proximal point method for multiobjective quasiconvex minimization," Annals of Operations Research, Springer, vol. 316(2), pages 1445-1470, September.
    • Handle: RePEc:spr:annopr:v:316:y:2022:i:2:d:10.1007_s10479-020-03622-8
    DOI: 10.1007/s10479-020-03622-8
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    References listed on IDEAS

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    14. Papa Quiroz, E.A. & Roberto Oliveira, P., 2012. "An extension of proximal methods for quasiconvex minimization on the nonnegative orthant," European Journal of Operational Research, Elsevier, vol. 216(1), pages 26-32.
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