Tucker's well-known combinatorial lemma states that for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {1,2,...n,-1,-2,....-n} with the property that antipodal vertices on the...

In this paper we present a method for using rational expectations in a linear-quadratic optimizationframework. Following the approach put forward by Sims, we solve the model through a QZdecomposition, which is generally easier to implement than the more widely used method of Blanchardand Kahn.

A necessary condition - the Principle of Fermat-Lagrange - is offered for mixed smooth-convexoptimization problems. This generalizes and unifies most of the known necessary conditions forconcrete finite and infinite dimensional optimization problems of interest. The new idea in comparisonwith...

In this paper we consider optimization problems defined by a quadraticobjective function and a finite number of quadratic inequality constraints.Given that the objective function is bounded over the feasible set, we presenta comprehensive study of the conditions under which the optimal solution...

In this paper we introduce several classes of generalized convexfunctions already discussed in the literature and show the relationbetween those function classes. Moreover, for some of those functionclasses a Farkas-type theorem is proved. As such this paper unifiesand extends results existing...

Many economic and social situations can be represented by a digraph. Both axiomatic and iterativemethods to determine the strength or power of all the nodes in a digraph have been proposed inthe literature. We propose a new method, where the power of a node is determined by both thenumber of its...