Second-Order Set-Valued Directional Derivatives of the Marginal Map in Parametric Vector Optimization Problems.
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| Title: | Second-Order Set-Valued Directional Derivatives of the Marginal Map in Parametric Vector Optimization Problems. |
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| Authors: | Bao, Nguyen Xuan Duy1,2 (AUTHOR) nxdbao@hcmut.edu.vn, Khanh, Phan Quoc3 (AUTHOR) phanquockhanh@tdtu.edu.vn, Tung, Nguyen Minh4 (AUTHOR) tungnm@hub.edu.vn |
| Source: | Journal of Optimization Theory & Applications. Mar2025, Vol. 204 Issue 3, p1-20. 20p. |
| Subjects: | Multi-objective optimization, Directional derivatives, Mathematical mappings, Computational mathematics, Mathematical optimization, Set-valued maps |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| 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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 00223239 |
| DOI: | 10.1007/s10957-025-02606-7 |
