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New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization

Author

Listed:
  • G. Haeser

    (University of São Paulo)

  • A. Ramos

    (Federal University of Paraná)

Abstract

In this paper, we present and discuss new constraint qualifications to ensure the validity of well-known second-order properties in nonlinear optimization. Here, we discuss conditions related to the so-called basic second-order condition, where a new notion of polar pairing is introduced in order to replace the polar operation, useful in the first-order case. We then proceed to define our second-order constraint qualifications, where we present an approach similar to the Guignard constraint qualification in the first-order case.

Suggested Citation

  • G. Haeser & A. Ramos, 2020. "New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 494-506, February.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:2:d:10.1007_s10957-019-01603-x
    DOI: 10.1007/s10957-019-01603-x
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    References listed on IDEAS

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    1. Aram Arutyunov & Fernando Lobo Pereira, 2006. "Second-Order Necessary Optimality Conditions for Problems Without A Priori Normality Assumptions," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 1-12, February.
    2. Nguyen Quang Huy & Nguyen Van Tuyen, 2016. "New Second-Order Optimality Conditions for a Class of Differentiable Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 27-44, October.
    3. Giorgio Giorgi, 2018. "A Guided Tour in Constraint Qualifications for Nonlinear Programming under Differentiability Assumptions," DEM Working Papers Series 160, University of Pavia, Department of Economics and Management.
    Full references (including those not matched with items on IDEAS)

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