Sufficient Optimality Conditions for Optimal Control Problems with State Constraints
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It is well-known in optimal control theory that the maximum principle, in general, furnishes only necessary optimality conditions for an admissible process to be an optimal one. It is also well-known that if a process satisfies the maximum principle in a problem with convex data, the maximum principle turns to be likewise a sufficient condition. Here an invexity type condition for state constrained optimal control problems is defined and shown to be a sufficient optimality condition. Further, it is demonstrated that all optimal control problems where all extremal processes are optimal necessarily obey this invexity condition. Thus optimal control problems which satisfy such a condition constitute the most general class of problems where the maximum principle becomes automatically a set of sufficient optimality conditions.
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Generalized convexity, optimal control, state constraints, sufficient optimality conditions
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Inglês
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Numerical Functional Analysis and Optimization, v. 40, n. 8, p. 867-887, 2019.
