A second-order variational inclusion for control systems under state constraints is derived and applied to investigate necessary optimality conditions for the Mayer optimal control problem. A new pointwise condition verified by the adjoint state of the maximum principle is obtained as well as a second-order necessary optimality condition in the integral form. Finally, a new sufficient condition...

It well known that the Pontryagin maximum principle is a necessary optimality condition for control problems. For linear control problems, it is also a sufficient condition, but for a nonlinear control problems in common form, it is not. We found a class of nonlinear control problems for which the Pontryagin maximum principle is also a sufficient optimality condition. This is a class of problem...

In this paper,we consider the restless bandit problem, which is one of the most well-studied generalizations of the celebrated stochastic multi-armed bandit problem in decision theory. However, it is known be PSPACE-Hard to approximate to any non-trivial factor. Thus the optimality is very difficult to obtain due to its high complexity. A natural method is to obtain the greedy policy considerin...

We consider the problem of minimizing a Lipschitz differentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize 1/L satisfies the L-stationarity optimality condition that was introduced in [3]. In this paper we ...

We consider the problem of minimizing a Lipschitz di erentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize 1/L satis es the L-stationarity optimality condition that was introduced in [3]. In this paper we in...