Geodesic
Stability theorem and extremum conditions for abnormal problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 291 (2015), pp. 10-29

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove a generalized inverse function theorem in a neighborhood of a singular point of a mapping. As corollaries to this theorem, we obtain an inverse function theorem, an error bound theorem, and a tangent cone theorem that extend and strengthen the corresponding classical results in the irregular case. Using these corollaries, we establish necessary extremum conditions that are meaningful for abnormal problems. 
@article{TM_2015_291_a1,
     author = {E. R. Avakov},
     title = {Stability theorem and extremum conditions for abnormal problems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {10--29},
     publisher = {mathdoc},
     volume = {291},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_291_a1/}
}
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E. R. Avakov. Stability theorem and extremum conditions for abnormal problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 291 (2015), pp. 10-29. http://geodesic.mathdoc.fr/item/TM_2015_291_a1/