Geodesic
Lagrange's principle in extremum problems with constraints
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 68 (2013) no. 3, pp. 401-433

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In this paper a general result concerning Lagrange's principle for so-called smoothly approximately convex problems is proved which encompasses necessary extremum conditions for mathematical and convex programming, the calculus of variations, Lyapunov problems, and optimal control problems with phase constraints. The problem of local controllability for a dynamical system with phase constraints is also considered. In an appendix, results are presented that relate to the development of a ‘Lagrangian approach’ to problems where regularity is absent and classical approaches are meaningless. Bibliography: 33 titles.
Keywords: extremum problem, optimal control, phase constraints, controllability, abnormality.
Mots-clés : mix 
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     author = {E. R. Avakov and G. G. Magaril-Il'yaev and V. M. Tikhomirov},
     title = {Lagrange's principle in extremum problems with constraints},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2013_68_3_a1/}
}
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E. R. Avakov; G. G. Magaril-Il'yaev; V. M. Tikhomirov. Lagrange's principle in extremum problems with constraints. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 68 (2013) no. 3, pp. 401-433. http://geodesic.mathdoc.fr/item/RM_2013_68_3_a1/