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<p>In this paper, we investigate a class of nonsmooth multiobjective quasiconvex optimization problems (NMOPs). By employing the limiting subdifferential, we introduce an inexact inertial proximal point algorithm with quasi-distance (IIPPA-QD) to solve an NMOP. We first justify the well-definedness of the sequence generated by the IIPPA-QD algorithm and then show that every cluster point of the sequence generated by our method is a Pareto critical point of NMOP. Especially, if the components of the objective function of NMOP are convex, then such a cluster point becomes a weak Pareto optimal solution of the underlying problem. We also establish a finite termination rule for the IIPPA-QD algorithm under additional conditions. Finally, we implement the IIPPA-QD algorithm on several numerical examples and a practical model from a class of facility location problems, demonstrating the effectiveness and competitiveness of our method.</p>

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Convergence analysis of an inexact inertial proximal point algorithm for multiobjective quasiconvex optimization problems

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Balendu Bhooshan Upadhyay,
  • Subham Poddar,
  • Thai Doan Chuong

摘要

In this paper, we investigate a class of nonsmooth multiobjective quasiconvex optimization problems (NMOPs). By employing the limiting subdifferential, we introduce an inexact inertial proximal point algorithm with quasi-distance (IIPPA-QD) to solve an NMOP. We first justify the well-definedness of the sequence generated by the IIPPA-QD algorithm and then show that every cluster point of the sequence generated by our method is a Pareto critical point of NMOP. Especially, if the components of the objective function of NMOP are convex, then such a cluster point becomes a weak Pareto optimal solution of the underlying problem. We also establish a finite termination rule for the IIPPA-QD algorithm under additional conditions. Finally, we implement the IIPPA-QD algorithm on several numerical examples and a practical model from a class of facility location problems, demonstrating the effectiveness and competitiveness of our method.