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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 73, 2024 - Issue 6
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Research Article

On strong second-order necessary optimality conditions under relaxed constant rank constraint qualification

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Pages 1993-2005 | Received 06 Sep 2022, Accepted 28 Feb 2023, Published online: 10 Mar 2023

References

  • Abadie J. On the Kuhn-Tucker theorem. In: Abadie J, editor. Nonlinear programming. Amsterdam: North Holland; 1967. p. 19–36.
  • Andreani R, Haeser G, Schuverdt ML, et al. A relaxed constant positive linear dependence constraint qualification and applications. Math Program. 2012;135(1–2):255–273.
  • Bazaraa MS, Sherali HD, Shetty CM. Nonlinear programming theory and algorithms. 3rd ed. NJ: John Wiley & Sons; 2006.
  • Bertsekas DP. Nonlinear programming. 2nd ed. Belmont, MA: Athena Scientific; 1999.
  • Guignard M. Generalized Kuhn-Tucker conditions for mathematical programming problems in a Banach space. SIAM J Control. 1969;7(2):232–241.
  • Janin R. Directional derivative of the marginal function in nonlinear programming. In: Fiacco AV, editor. Sensitivity, stability and parametric analysis; Vol. 21; Berlin: Math. Program. Stud.; 1984. p. 110–126.
  • Mangasarian OL, Fromovitz S. The Fritz John necessary optimality conditions in the presence of equality and inequality constraints. J Math Anal Appl. 1967;17(1):37–47.
  • Minchenko L: Stakhovski S. On relaxed constant rank regularity condition in mathematical programming. Optimization. 2011;60(4):429–440.
  • Nocedal J, Wright SJ. Numerical optimization. Springer series in operations research; 2nd ed. Springer-Verlag; 2006.
  • Qi L, Wei Z. On the constant positive linear dependence condition and its application to SQP methods. SIAM J Optim. 2000;10(4):963–981.
  • Andreani R, Echagüe CE, Schuverdt ML. Constant-rank condition and second-order constraint qualification. J Optim Theory Appl. 2010;146(2):255–266.
  • Minchenko L, Leschov A. On strong and weak second-order necessary optimality conditions for nonlinear programming. Optimization. 2016;65(9):1693–1702.
  • Minchenko L, Stakhovski S. Parametric nonlinear programming problems under the relaxed constant rank condition. SIAM J Optim. 2011;21(1):314–332.
  • Andreani R, Behling R, Haeser G, et al. On second-order optimality conditions in nonlinear optimization. Optim Methods Softw. 2017;32(1):22–38.
  • Andreani R, Haeser G, Ramos A, et al. A second-order sequential optimality condition associated to the convergence of optimization algorithms. IMA J Numer Anal. 2017;37(4):1902–1929.
  • Malliavin P. Géométrie différentielle intrinsèque. Paris: Herman; 1972.
  • Andreani R, Martínez JM, Ramos A, et al. A cone-continuity constraint qualification and algorithmic consequences. SIAM J Optim. 2016;26(1):96–110.
  • Andreani R, Martínez JM, Schuverdt ML. On the relation between constant positive linear dependence condition and quasinormality constraint qualification. J Optim Theory Appl. 2005;125(2):473–483.

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