We consider the simplest optimal control problem with one nonregular mixed constraint $G(x,u)\le0,$ i.e., such a that gradient $G_u(x, u)$ can vanish on surface $G = 0.$ Using Dubovitskii--Milyutin theorem approximate separation of convex cones, we prove first order necessary condition for weak minimum in form so-called local principle, which is formulated terms functions bounded variation, int...

Branch and bound methods for finding all solutions of a global optimization problem in a box frequently have the difficulty that subboxes containing no solution cannot be easily eliminated if they are close to the global minimum. This has the effect that near each global minimum, and in the process of solving the problem also near the currently best found local minimum, many small boxes are cre...

Traditional genetic algorithm trapped into the local minimum easily. Therefore, based on a simple genetic algorithm and combine the base ideology of orthogonal design method then applied it to the population initialization, using the intergenerational elite mechanism, as well as the introduction of adaptive local search operator to prevent trapped into the local minimum and improve the converge...

We study two nonlocal variational problems in this paper. One models micro-phase separation of diblock copolymers and the other models solid-solid phase transformations that lead to fine structures. We study a parameter range where the problems can be approximated by their asymptotic limits. We find all the local minimum solutions of the limiting problems. Because these local minima are isolate...