Some Inequalities of the Uniform Ergodicity and Strong Stability of Homogeneous Markov Chains

2000 Mathematics Subject Classification: 60J45, 60K25

Stability of the Inventory-Backorder Process in the (R; S) Inventory/Production Model

2000 Mathematics Subject Classification: 60G52, 90B30.

Strong-weak Stackelberg Problems in Finite Dimensional Spaces

We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation results when the parameter ǫ goes to zero. Finally, as an example, we consider an optimization problem associated to a best bound given in [2] for a system of nondifferentiable convex inequalities.