First and second order sufficient optimality conditions in mathematical programming and optimal control

First and second order sufficient conditions are given for infinite-dimensional programming problems with constraints defined by arbitrary closed convex cones. The sufficient conditions are formulated by means of two norms and, thereby, are applicable to optimal control problems with state constraints where the definiteness conditions can only hold in a weaker norm than that in which the functions involved are differentiable. The second order sufficient conditions yield an extension of the classical Riccati-type conditions.

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