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<p>This paper deals with a class of nonsmooth multiobjective quasiconvex optimization problems (abbreviated as, NMQOPs) in the framework of Hadamard manifolds. We introduce the inertial proximal point algorithm (abbreviated as, IPPA) in terms of Mordukhovich limiting subdifferential to solve NMQOP. We establish the well-definedness of the sequence generated by the IPPA algorithm. Subsequently, we derive that the sequence generated by the IPPA algorithm converges to the Pareto-Mordukhovich critical point of NMQOP. Moreover, we deduce that if the components of the objective function of NMQOP are geodesic convex, then the sequence converges to the weak Pareto optimal solution of NMQOP. In addition to this, we establish the finite termination of the IPPA algorithm under appropriate assumptions. Finally, we furnish several numerical examples to demonstrate the effectiveness and competitiveness of the IPPA algorithm. Some results of this paper are even new in the Euclidean space setting, while others improve the corresponding results derived in [Bento et al. Set-Valued Var. Anal. 22, 557-573 (2014)], [Apolinário et al. J. Global Optim. 64, 79–96 (2016)], [Papa Quiroz et al. J. Optim. Theory Appl. 186, 879–898 (2020)] for NMQOPs.</p>

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Inertial proximal point algorithm on Hadamard manifolds: convergence analysis and finite termination

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Balendu Bhooshan Upadhyay,
  • Subham Poddar,
  • Giuseppe Caristi,
  • David Barilla

摘要

This paper deals with a class of nonsmooth multiobjective quasiconvex optimization problems (abbreviated as, NMQOPs) in the framework of Hadamard manifolds. We introduce the inertial proximal point algorithm (abbreviated as, IPPA) in terms of Mordukhovich limiting subdifferential to solve NMQOP. We establish the well-definedness of the sequence generated by the IPPA algorithm. Subsequently, we derive that the sequence generated by the IPPA algorithm converges to the Pareto-Mordukhovich critical point of NMQOP. Moreover, we deduce that if the components of the objective function of NMQOP are geodesic convex, then the sequence converges to the weak Pareto optimal solution of NMQOP. In addition to this, we establish the finite termination of the IPPA algorithm under appropriate assumptions. Finally, we furnish several numerical examples to demonstrate the effectiveness and competitiveness of the IPPA algorithm. Some results of this paper are even new in the Euclidean space setting, while others improve the corresponding results derived in [Bento et al. Set-Valued Var. Anal. 22, 557-573 (2014)], [Apolinário et al. J. Global Optim. 64, 79–96 (2016)], [Papa Quiroz et al. J. Optim. Theory Appl. 186, 879–898 (2020)] for NMQOPs.