In this paper we consider a homogeneous analytic center cutting plabne method in a projective space. We describe a general scheme that uses a homogeneous oracle and computes an approximate analytic center at each iteration. This technique is applied to a convex feasibility problem, to...

In this paper we present several "infeasible-start" path-following and potential-reduction primal-dual interior-point methods for non-linear conic problems. These methods try to find a recession direction of the feasible set of a self-dual homogeneous primal-dual problem.

WE analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when the cuts are central. The dircetion is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal...

Stochastic programs inevitably get huge if they are to model real life problems accurately. Nowadays only massive parallel machines can solve them but at a cost few decision makers can afford. We report hereon a deterministic equivalent linear programming model of 1,111,112 constraints and...

This paper addresses the issues involved with an interior point-based decomposition applied to the solution of linear programs with a block-angular structure. Unlike classicla decomposition schemes that use the simplex method to solve subproblems, the approach presented in this paper employs a...

Mixture sets were introduced by Herstein and Milnor (1953) into decision theory, where they are still widely used. This note clarifies the formal connection between mixture sets and convex sets. The results suggest that the former concept might be unnecessary for decision- theoretic purposes.

The critical role of free entry to correct inherent deviance behavior has been stressed by Vanek (1970), Meade (1972) amongst others. The equivalence theorem (Dreze 1976) defines that labour and entrepreneurial management both lead to the same Pareto optimal equilibrium provided that there is...

The paper proposes an original class of conditionally heteroskedastic models aimed to capture a new concept of asymmetry. Not only past up and down moves of stock market returns have different impacts on the conditional variance, but also, positive and negative changes are governed by different...

If a solution (on a closed family of games) satisfies dummy axiom (DUM) and independance of irrelevant strategies (IIS) then it also satisfies consistency (CONS) (proposition 2.21, Peleg and Tijs, 1996). The converse of this proposition is not true: CONS implies neither DUM nor IIS as shown in...

The notion of disapprobation is defined. It is designed to capture some features of misspecification in a decision-theoretic framework. Moreover, it is a sample-based notion so it is well-suited for the study of misspecification in Bayesian contexts. Some elementary examples of disapprobation...