On Nonsmooth Multiobjective Semi-Infinite Programming with Switching Constraints Using Convexificators

Rishabh Pandey, Yogendra Pandey, Vinay Singh () and Anjali Rawat
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Rishabh Pandey: National Institute of Technology Mizoram, Department of Mathematics
Yogendra Pandey: Satish Chandra College, Department of Mathematics
Vinay Singh: National Institute of Technology Mizoram, Department of Mathematics
Anjali Rawat: National Institute of Technology Mizoram, Department of Mathematics

Chapter 20 in Convex and Variational Analysis with Applications, 2026, pp 449-474 from Springer

Abstract: Abstract This work investigates a nonsmooth multiobjective semi-infinite programming problem with switching constraints $$({\mathcal {M}}{\mathcal {S}}{\mathcal {P}}{\mathcal {S}}{\mathcal {C}})$$ ( M S P S C ) . Using convexificators and under the nonsmooth Abadie constraint qualification, we derive necessary optimality conditions in the form of $$\textbf{M}$$ M -stationary. Furthermore, under generalized convexity conditions expressed through the properties of convexificators, we establish sufficient conditions for optimality. For the original $${\mathcal {M}}{\mathcal {S}}{\mathcal {P}}{\mathcal {S}}{\mathcal {C}}$$ M S P S C problem, we formulate a Mond-Weir-type dual model and prove both weak and strong duality results between the primal and dual problems. Finally, numerical examples are provided to demonstrate the applicability of the theoretical findings to $${\mathcal {M}}{\mathcal {S}}{\mathcal {P}}{\mathcal {S}}{\mathcal {C}}$$ M S P S C .

Keywords: Switching constraints; Multiobjective optimization; Stationarity; Optimality conditions; Duality (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-032-07860-5_20

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DOI: 10.1007/978-3-032-07860-5_20

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