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On second-order derivatives of the efficient point multifunction in parametric vector optimization problems

Pham Thanh-Hung, Nguyen Thanh-Sang

Control and Cybernetics

2023

Vol. 52, No. 4

381--403

In this paper, we establish formulae for inner and outer evaluation of the second-order contingent derivative of index nu of the efficient point multifunction in parametric vector optimization problems. The results contained in this paper extend the results of Chuong (2013a) to the second-order sensitivity analysis case. On the other hand, examples are provided for purposes of analyzing and illustrating the obtained results. Concerning the potential domain of application, the functioning of the majority of economic systems depends on a set of indicators (criteria), i.e., the substance of economic systems includes multiple criteria and only the lack of mathematical methods in solving the problems of vector optimization is an obstacle to the effective use of the respective models. Therefore, the study of vector optimization problems is necessary and has practical significance.