Second-Order Set-Valued Directional Derivatives of the Marginal Map in Parametric Vector Optimization Problems

Nguyen Xuan Duy Bao (), Phan Quoc Khanh () and Nguyen Minh Tung ()
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Nguyen Xuan Duy Bao: University of Technology
Phan Quoc Khanh: Ton Duc Thang University
Nguyen Minh Tung: Ho Chi Minh University of Banking

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 3, No 10, 20 pages

Abstract: Abstract We study second-order differential sensitivity in parametrized vector optimization problems with inclusion constraints. First, we consider a set-valued unconstrained problem and establish a sufficient condition for the second-order directional Dini derivative of the marginal map to be equal to the minimum of that of the objective map. We then extend our research to vector optimization problems with general inclusion constraints and demonstrate that the first- and second-order directional Dini derivatives of the objective image map are equal to the union of those of the objective map. Using advanced proof techniques, we derive a formula for the second-order directional Dini derivative of the marginal map and prove the second-order semi-derivability of the feasible objective and marginal/efficient-value maps. Examples are provided to illustrate the novelty and depth of our results.

Keywords: Differential sensitivity; Directional Dini derivative; Marginal mapping; Parametric optimization; 90C29; 90C31; 90C30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02606-7

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