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<p>This paper deals with a class of uncertain multiobjective semi-infinite programming problems with equilibrium constraints (UMSIPECs). We formulate the associated robust counterpart of UMSIPEC, that is, the robust multiobjective semi-infinite programming problem with equilibrium constraints (RMSIPEC). By employing the powerful tools of Mordukhovich limiting subdifferentials, we introduce the notion of generalized robust limiting constraint qualification (GRLCQ) for RMSIPEC to derive the necessary criteria for local weak Pareto efficiency of RMSIPEC. Moreover, by employing the notion of generalized convexity, we establish sufficient optimality criteria for RMSIPEC. Furtherm‘ore, we formulate the Mond-Weir-type dual problem for RMSIPEC and establish several duality results that relate the primal problem RMSIPEC and its corresponding dual problem. Several examples are furnished to demonstrate the significance of the results established in this paper.</p>

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Pareto efficiency criteria and duality for robust multiobjective semi-infinite programming problems with equilibrium constraints

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Balendu Bhooshan Upadhyay,
  • Subham Poddar,
  • Rupesh K. Pandey,
  • Atefeh Hassani Bafrani,
  • Michael Morabito,
  • Giuseppe Caristi

摘要

This paper deals with a class of uncertain multiobjective semi-infinite programming problems with equilibrium constraints (UMSIPECs). We formulate the associated robust counterpart of UMSIPEC, that is, the robust multiobjective semi-infinite programming problem with equilibrium constraints (RMSIPEC). By employing the powerful tools of Mordukhovich limiting subdifferentials, we introduce the notion of generalized robust limiting constraint qualification (GRLCQ) for RMSIPEC to derive the necessary criteria for local weak Pareto efficiency of RMSIPEC. Moreover, by employing the notion of generalized convexity, we establish sufficient optimality criteria for RMSIPEC. Furtherm‘ore, we formulate the Mond-Weir-type dual problem for RMSIPEC and establish several duality results that relate the primal problem RMSIPEC and its corresponding dual problem. Several examples are furnished to demonstrate the significance of the results established in this paper.