Jul 2026· Reserche operationelle· Vol 60, pp. 2627-2640· 0 citations
TL;DR
A generalized Lagrangian function is introduced, and the feasible solutions of the data uncertainty problem are characterized in terms of saddle points of the Lagrangian function.
Abstract
The main purpose of this paper is to study a nonsmooth vector programming problem affected by data uncertainty. The partial ordering in objective image space is induced by a proper cone lying in $n-$dimensional Euclidean space. The Clarke's generalized subgradients and generalized pseudoquasi-convexity assumptions are used to extract Pareto efficient solutions. Then Karush-Kuhn-Tucker (KKT) optimality conditions over cones and the generalized convexity assumptions are employed to find a Primal-Dual relationship between the uncertainty problem and a Mond-Weir type dual. Lastly, a generalized Lagrangian function is introduced, and the feasible solutions of the data uncertainty problem are characterized in terms of saddle points of the Lagrangian function.
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