Abstract In an earlier analysis of strong variation algorithms for optimal control problems with endpoint inequality constraints, Mayne and Polak provided conditions under which accumulation points satisfy a condition requiring certain optimality function, used in the to generate search directions, be nonnegative all controls. The aim this paper is clarify nature condition, we call first-order ...

An offset discretization of a set $$X \subset {\mathbb {R}}^n$$ is obtained by taking the integer points inside closed neighborhood X certain radius. In this work we determine minimum threshold for radius, beyond which an arbitrary (possibly disconnected) always connected. The results hold broad class disconnected subsets $${\mathbb and generalize several previous results. We also extend our to...