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Second-Order Enhanced Optimality Conditions and Constraint Qualifications

Author

Listed:
  • Kuang Bai

    (The Hong Kong Polytechnic University)

  • Yixia Song

    (Southern University of Science and Technology)

  • Jin Zhang

    (Southern University of Science and Technology, Peng Cheng Laboratory)

Abstract

In this paper, we study second-order necessary optimality conditions for smooth nonlinear programming problems. Employing the second-order variational analysis and generalized differentiation, under the weak constant rank (WCR) condition, we derive an enhanced version of the classical weak second-order Fritz–John condition which contains some new information on multipliers. Based on this enhanced weak second-order Fritz–John condition, we introduce the weak second-order enhanced Karush–Kuhn–Tucker condition and propose some associated second-order constraint qualifications. Finally, using our new second-order constraint qualifications, we establish new sufficient conditions for the existence of a Hölder error bound condition.

Suggested Citation

  • Kuang Bai & Yixia Song & Jin Zhang, 2023. "Second-Order Enhanced Optimality Conditions and Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1264-1284, September.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:3:d:10.1007_s10957-023-02276-3
    DOI: 10.1007/s10957-023-02276-3
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    References listed on IDEAS

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    6. R. Andreani & J. M. Martinez & M. L. Schuverdt, 2005. "On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 473-483, May.
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