5. Shooting algorithm and problem discretization

5.1 Problems without constraints

It is assumed here that $u \mapsto F (u)$ has a weak minimum $\bar{u}$ , a continuous function of time, satisfying the following strong (time-uniform) Legendre-Clebsch condition, where I _d is the identity matrix (compare to the necessary condition

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Shooting algorithm and problem discretization

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Second-order optimality conditions

Bibliography

(1) - ARONNA (M.S.), BONNANS (J.F.), MARTINON (P.) - A shooting algorithm for optimal control problems with singular arcs - J. Optim. Theory Appl., 158 (2) : 419-459 (2013).
(2) - BARDI (M.), CAPUZZO-DOLCETTA (I.) - Optimal control and viscosity solutions...