Geodesic
Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems
de Pinho, Maria do Rosário  ; Ferreira, Maria Margarida ; Fontes, Fernando1 
1 Officina Mathematica, Universidade do Minho, 4800-058 Guimarães, Portugal
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 4, pp. 614-632

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Necessary conditions of optimality in the form of Unmaximized Inclusions (UI) are derived for optimal control problems with state constraints. The conditions presented here generalize earlier optimality conditions to problems that may be nonconvex. The derivation of UI-type conditions in the absence of the convexity assumption is of particular importance when deriving necessary conditions for constrained problems. We illustrate this feature by establishing, as an application, optimality conditions for problems that in addition to state constraints incorporate mixed state-control constraints.

DOI : 10.1051/cocv:2005020
Classification : 49K15
Keywords: optimal control, state constraints, nonsmooth analysis, Euler-Lagrange inclusion

de Pinho, Maria do Rosário  ; Ferreira, Maria Margarida  ; Fontes, Fernando 1

1 Officina Mathematica, Universidade do Minho, 4800-058 Guimarães, Portugal 
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de Pinho, Maria do Rosário; Ferreira, Maria Margarida; Fontes, Fernando. Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 4, pp. 614-632. doi: 10.1051/cocv:2005020

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