# Volume 08 (2004) No. 1

## Volume 08 (2004) No. 1

### Multiobjective Markov control processes: a linear programming approach

Onésimo Hernández-Lerma and Rosario Romera

**Abstract:**

This paper studies discrete-time multiobjective Markov control processes (MCPs) on Borel spaces and unbounded costs. Under mild assumptions, it shows the existence of Pareto policies, which, as in multiobjective optimization problems, are also characterized as optimal policies for a certain class of single-objective (or "scalar") MCPs. A similar result is obtained for *strong* Pareto policies, which are Pareto policies whose cost vector is the closest, in the Euclidean norm, to the virtual minimum. To obtain these results, the basic idea is to transform the multiobjective MCP into an equivalent *multiobjective measure problem* (MMP). In addition, MMP is restated as a primal multiobjective *linear program* and it is shown that solving the *dual program* is in fact the same as solving the scalarized MCPs. A multiobjective LQ example illustrates the main results.

### Tutte uniqueness of locally grid graphs

D. Garijo, A Márquez and M. P. Revuelta

**Abstract:**

A graph is said to be locally grid if the structure around each of its vertices is a $3 \times 3$ grid. As a follow up of the research initiated in [4] and [3], we prove that most locally grid graphs are uniquely determined by their Tutte polynomial.

### No-inmersión de espacios lente

Enrique Torres Giese

**Abstract:**

Con herramientas básicas como la sucesión espectral de Serre y los cuadrados de Steenrod se obtienen resultados de no-inmersión de espacios lente de dimensión $2n+1$ y torsión $2^m$. En la situación $\alpha (n) =1$, donde $\alpha (n)$ es el número de 1's en la expresión binaria de $n$, el resultado es óptimo.