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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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    1. Kaiwen Meng & Xiaoqi Yang, 2015. "First- and Second-Order Necessary Conditions Via Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 720-752, June.
    2. 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.
    3. R. Andreani & C. E. Echagüe & M. L. Schuverdt, 2010. "Constant-Rank Condition and Second-Order Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 255-266, August.
    4. Gianni Di Pillo & Stefano Lucidi & Laura Palagi, 2005. "Convergence to Second-Order Stationary Points of a Primal-Dual Algorithm Model for Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 897-915, November.
    5. L. Minchenko & A. Tarakanov, 2011. "On Error Bounds for Quasinormal Programs," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 571-579, March.
    6. D.P. Bertsekas & A.E. Ozdaglar, 2002. "Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 287-343, August.
    7. Frank H. Clarke, 1976. "A New Approach to Lagrange Multipliers," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 165-174, May.
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