Stopped Markov decision processes with multiple constraints

In this paper, a optimization problem for stopped Markov decision processes with vector-valued terminal reward and multiple running cost constraints is considered. Applying the idea of occupation measures and using the scalarization technique for vector maximization problems we obtain the equivalent Mathematical Programming problem and show the existence of a Pareto optimal pair of stationary policy and stopping time requiring randomization in at most k states, where k is the number of constraints. Moreover Lagrange multiplier approaches are considered. The saddle-point statements are given, whose results are applied to obtain a related parametric Mathematical Programming, by which the problem is solved. Numerical examples are given.