Showing papers by "Onésimo Hernández-Lerma published in 2006"
TL;DR: A survey of recent results on continuous-time Markov decision processes withunbounded transition rates, and reward rates that may be unbounded from above and from below can be found in this paper.
Abstract: This paper is a survey of recent results on continuous-time Markov decision processes (MDPs) withunbounded transition rates, and reward rates that may beunbounded from above and from below. These results pertain to discounted and average reward optimality criteria, which are the most commonly used criteria, and also to more selective concepts, such as bias optimality and sensitive discount criteria. For concreteness, we consider only MDPs with a countable state space, but we indicate how the results can be extended to more general MDPs or to Markov games.
81 citations
14 Jun 2006
TL;DR: This paper analyzes the convergence of metaheuristics used for multiobjective optimization problems in which the transition probabilities use a uniform mutation rule and proves that these algorithms converge only if elitism is used.
Abstract: This paper analyzes the convergence of metaheuristics used for multiobjective optimization problems in which the transition probabilities use a uniform mutation rule. We prove that these algorithms converge only if elitism is used.
30 citations
TL;DR: Conditions for the existence of bias optimal policies in a class of continuous-time controlled Markov chains with unbounded reward and transition rates are given and several characterizations of bias optimality are proposed.
Abstract: In this paper we give conditions for the existence of bias optimal policies in a class of continuous-time controlled Markov chains with unbounded reward and transition rates. Several characterizations of bias optimality are proposed. We also introduce new sets of conditions ensuring uniform exponential ergodicity of continuous-time controlled Markov chains.
29 citations
TL;DR: This paper considers constrained noncooperative N-person stochastic games with discounted cost criteria, and shows the existence of Nash equilibria for constrained games with a finite state space (and compact actions space), and extends that existence result to a class of constrained games which can be “approximated” by constrainedGames with finitely many states and compact action spaces.
Abstract: In this paper, we consider constrained noncooperative N-person stochastic games with discounted cost criteria. The state space is assumed to be countable and the action sets are compact metric spaces. We present three main results. The first concerns the sensitivity or approximation of constrained games. The second shows the existence of Nash equilibria for constrained games with a finite state space (and compact actions space), and, finally, in the third one we extend that existence result to a class of constrained games which can be “approximated” by constrained games with finitely many states and compact action spaces. Our results are illustrated with two examples on queueing systems, which clearly show some important differences between constrained and unconstrained games.
25 citations
TL;DR: In this paper, a simulated annealing algorithm for multiobjective optimization problems is proposed and the algorithm is shown to converge asymptotically, that is, the Markov chain that describes the algorithm converges with probability one to the optimal set.
Abstract: In this paper we consider a simulated annealing algorithm for multiobjective optimization problems. With a suitable choice of the acceptance probabilities, the algorithm is shown to converge asymptotically, that is, the Markov chain that describes the algorithm converges with probability one to the Pareto optimal set.
15 citations
TL;DR: Conditions are given under which the MT problem is solvable and an optimal solution can be obtained as the weak limit of a sequence of optimal solutions to suitably approximating MT problems.
Abstract: This paper studies the Monge--Kantorovich mass transfer (MT) problem on metric spaces, with possibly unbounded "cost" function. Conditions are given under which the MT problem is solvable and, furthermore, an optimal solution can be obtained as the weak limit of a sequence of optimal solutions to suitably approximating MT problems.
7 citations