Free Access
Volume 27, 2021
Article Number 9
Number of page(s) 22
Published online 03 March 2021
  1. J. Abadie, On the Kuhn-Tucker theorem, in Nonlinear Programming (NATO Summer School, Menton, 1964). North-Holland, Amsterdam (1967) 19–36. [Google Scholar]
  2. R. Abraham, J.E. Marsden and T. Ratiu, Manifolds, tensor analysis, and applications. Vol. 75 of Applied Mathematical Sciences, second ed. Springer-Verlag, New York (1988). [CrossRef] [Google Scholar]
  3. R. Andreani, R. Behling, G. Haeser and P.J.S. Silva, On second-order optimality conditions in nonlinear optimization. Optim. Methods Softw. 32 (2017) 22–38. [Google Scholar]
  4. R. Andreani, C.E. Echagüe and M.L. Schuverdt, Constant-rank condition and second-order constraint qualification. J. Optim. Theory Appl. 146 (2010) 255–266. [Google Scholar]
  5. R. Andreani, N.S. Fazzio, M.L. Schuverdt and L.D. Secchin, A sequential optimality condition related to the quasi-normality constraint qualification and its algorithmic consequences. SIAM J. Optim. 29 (2019) 743–766. [Google Scholar]
  6. R. Andreani, G. Haeser, M.L. Schuverdt and P.J.S. Silva, A relaxed constant positive linear dependence constraint qualification and applications. Math. Program. 135 (2012) 255–273. [Google Scholar]
  7. R. Andreani and P. Silva, Constant rank constraint qualifications: a geometric introduction. Pesquisa Operacional 34 (2014) 481–494. [Google Scholar]
  8. E.M. Bednarczuk, L.I. Minchenko and K.E. Rutkowski, On lipschitz-like continuity of a class of set-valued mappings. Optimization 62 (2019) 2535–2549. [Google Scholar]
  9. R. Bergmann and R. Herzog, Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds. Preprint arXiv:1804.06214 (2018). [Google Scholar]
  10. J.F. Bonnans and A. Shapiro, Perturbation analysis of optimization problems. Springer Series in Operations Research. Springer-Verlag, New York (2000). [Google Scholar]
  11. W.M. Boothby, An introduction to differentiable manifolds and Riemannian geometry. Vol. 120 of Pure and Applied Mathematics, second ed. Academic Press, Inc., Orlando, FL (1986). [Google Scholar]
  12. E. Börgens, C. Kanzow, P. Mehlitz and G. Wachsmuth, New Constraint Qualifications for Optimization Problems in Banach Spaces based on Cone Continuity Properties. Preprint arXiv:1912.06531 (2019). [Google Scholar]
  13. F. Deutsch, Best approximation in inner product spaces. Vol. 7 of CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. Springer-Verlag, New York (2001). [Google Scholar]
  14. J. Gallier and J. Quaintance, Linear Algebra and Optimization with Applications to Machine Learning: Volume I: Linear Algebra for Computer Vision, Robotics, and Machine Learning. World Scientific Publishing Co Pte Ltd (2020). [Google Scholar]
  15. R. Henrion and J.V. Outrata, Calmness of constraint systems with applications. Math. Program. 104 (2005) 437–464. [Google Scholar]
  16. A.D. Ioffe and V.M. Tihomirov, Theory of extremal problems. Vol. 6 of Studies in Mathematics and its Applications. Translated from the Russian by Karol Makowski. North-Holland Publishing Co., Amsterdam-New York (1979). [Google Scholar]
  17. R. Janin, Directional derivative of the marginal function in nonlinear programming. Springer Berlin Heidelberg, Berlin, Heidelberg (1984) 110–126. [Google Scholar]
  18. A.Y. Kruger, L. Minchenko and J.V. Outrata, On relaxing the mangasarian–fromovitz constraint qualification. Positivity 18 (2014) 171–189. [Google Scholar]
  19. S. Kurcyusz, On the existence and nonexistence of lagrange multipliers in Banach spaces. J. Optim. Theory Appl. 20 (1976) 81–110. [Google Scholar]
  20. W. Li, Abadie’s constraint qualification, metric regularity, and error bounds for differentiable convex inequalities. SIAM J. Optim. 7 (1997) 966–978. [Google Scholar]
  21. K. Maurin, Analysis. Part I. Elements, Translated from the Polish by Eugene Lepa. D. Reidel Publishing Co., Dordrecht-Boston, Mass.; PWN—Polish Scientific Publishers; Warsaw (1976). [Google Scholar]
  22. L. Minchenko, Note on Mangasarian–Fromovitz-like constraint qualifications. J. Optim. Theory Appl. 182 (2019) 1199–1204. [Google Scholar]
  23. L. Minchenko and S. Stakhovski, On relaxed constant rank regularity condition in mathematical programming. Optimization 60 (2011) 429–440. [Google Scholar]
  24. R. Narasimhan, Lectures on topics in analysis, Notes by M. S. Rajwade. Tata Institute of Fundamental Research Lectures on Mathematics, No. 34, Tata Institute of Fundamental Research, Bombay (1965). [Google Scholar]
  25. J.-P. Penot, On the existence of lagrange multipliers in nonlinear programming in banach spaces, in Optimization and Optimal Control, edited by A. Auslender, W. Oettli, and J. Stoer. Springer Berlin Heidelberg (1981) 89–104. [Google Scholar]
  26. S.M. Robinson, Stability theory for systems of inequalities. II. Differentiable nonlinear systems. SIAM J. Numer. Anal. 13 (1976) 497–513. [Google Scholar]
  27. M. Solodov, Constraint Qualifications. Wiley Encyclopedia of Operations Research and Management Science (2011). [Google Scholar]
  28. L. Székelyhidi, Ordinary and partial differential equations for the beginner. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2016). [Google Scholar]
  29. V.A. Zorich, Mathematical analysis. I, Universitext, second ed. Translated from the 6th corrected Russian edition, Part I, 2012 by Roger Cooke, With Appendices A–F and new problems translated by Octavio Paniagua T. Springer-Verlag, Berlin (2015). [Google Scholar]
  30. J. Zowe and S. Kurcyusz, Regularity and stability for the mathematical programming problem in Banach spaces. Appl. Math. Optim. 5 (1979) 49–62. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.