Rishabh Pandey, Yogendra Pandey, Vinay Singh, Optimality and duality conditions for nondifferentiable multiobjective semi-infinite programming with equilibrium constraints

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DOI: 10.23952/jano.8.2026.2.06
Volume 8, Issue 2, 1 August 2026, Pages 253-270

Abstract. In this paper, we investigate a nondifferentiable multiobjective semi-infinite mathematical programming problem with equilibrium constraints. We introduce a nonsmooth version of the $\partial^{T}$ -Abadie constraint qualification ( $\partial^{T}$ -ACQ) and propose $\partial^{T}$ -strong stationarity conditions based on tangential subdifferentials. We demonstrate that strong stationarity serves as a necessary optimality condition under $\partial^{T}$ -ACQ. Furthermore, we derive sufficient optimality conditions for this nonsmooth extremum problem, assuming that the involved functions are Dini generalized convex, characterized by their tangential subdifferentials. Additionally, we formulate the Mond–Weir dual problems and examine duality relations under Dini generalized convexity assumptions. To conclude, we present illustrative examples that demonstrate the effectiveness of our theoretical results.

How to Cite this Article:
R. Pandey, Y. Pandey, V. Singh, Optimality and duality conditions for nondifferentiable multiobjective semi-infinite programming with equilibrium constraints, J. Appl. Numer. Optim. 8 (2026), 253-270.