Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.9.2025.1.06

Volume 9, Issue 1, 1 February 2025, Pages 81-110

 

Abstract. In this study, we investigate an uncertain multiobjective optimization problem through a set-valued optimization problem, and introduce a Newton method to find robust weakly efficient points of the considered uncertain optimization problem. We assume that the problem under consideration has uncertainty only in the objective function, and the involved uncertainty set is of finite cardinality. Also, for each uncertain scenario, the components of the objective function of the problem are assumed to be twice continuously differentiable and locally strong convex. Utilizing the concept of a partition set from set optimization, we formulate a class of vector optimization problems to solve the formulated set optimization problem pertaining to the considered uncertain multiobjective optimization. We derive a Newton method to solve this class of vector optimization problems that facilitates generating a sequence of points whose any limit point is a weakly robust efficient solution of the considered problem. The proposed method is found to have a local superlinear convergence rate under standard hypotheses with a regularity condition. Additionally, assuming Lipschitz continuity of the Hessian of the objective function for all scenarios, we show local quadratic convergence of the method. Finally, we provide numerical examples to discuss and illustrate the performance of the proposed method.

 

How to Cite this Article:
D. Ghosh, N. Kishor, X. Zhao, A Newton method for uncertain multiobjective optimization problems with finite uncertainty sets, J. Nonlinear Var. Anal. 9 (2025), 81-110.