Second-Order KKT-Invexity in Continuous-Time Optimization

. In this paper, we adapt to the context of continuous-time optimization a concept of generalized convexity adequate to work with second-order stationary solutions, which are solutions that satisfy second-order necessary optimality conditions. We show that the second-order necessary optimality conditions become sufficient when the problem satisfies such a generalized convexity concept. We also show that, under a certain regularity assumption, this concept is as general as possible, in the sense that if the problem is such that every second-order stationary solution is an optimal solution, then the problem necessarily satisfies the generalized convexity concept.