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Higher-order set-valued Hadamard directional derivatives: calculus rules and sensitivity analysis of equilibrium problems and generalized equations

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  • Nguyen Minh Tung

    (Banking University of Ho Chi Minh City)

  • Nguyen Xuan Duy Bao

    (University of Science
    Vietnam National University)

Abstract

In this paper, we propose a notion of higher-order directional derivatives in the sense of Hadamard for set-valued maps, which is a natural extension of the classical directional derivatives. Some of the usual calculus rules, for unions, intersections, products, sums, and compositions are given under directional metric subregularity conditions. The Hadamard differentiability of the efficient value mapping and a formula to compute its derivative are also obtained. Then, we apply these derivatives to establish an implicit set-valued map theorem and employ it to higher-order sensitivity analysis of the solution mapping for a parametric vector equilibrium problem. Sensitivity for solutions to a parametric generalized equation is also investigated. Many examples are provided for analyzing and illustrating the obtained results.

Suggested Citation

  • Nguyen Minh Tung & Nguyen Xuan Duy Bao, 2022. "Higher-order set-valued Hadamard directional derivatives: calculus rules and sensitivity analysis of equilibrium problems and generalized equations," Journal of Global Optimization, Springer, vol. 83(2), pages 377-402, June.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:2:d:10.1007_s10898-021-01090-3
    DOI: 10.1007/s10898-021-01090-3
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    References listed on IDEAS

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