Maximal Convex Subgroups of the Automorphism Group of a Doubly Transitive Chain

We characterise all maximal convex l-subgroups of A(), the automorphismgroup of a doubly transitive chain of countable coterminality.We then determine, up to isomorphism, all doubly transitiveactions of the l-group A(). Finally, assuming the ContinuumHypothesis, we show that there exists an unbounded chain ofproper prime subgroups of A().     

Critical angles in polyhedral convex cones: numerical and statistical considerations

This work concerns the numerical computation of critical angles in polyhedral convex cones. The set of proper critical angles is evaluated explicitly by solving a series of generalized eigenvalue problems involving the generators of the cone. The local maximal angles are identified by using a necessary condition for local maximality. The expected numbers of critical angles in random polyhedral convex cones are estimated experimentally.     

Solidity indices for convex cones

The issue addressed in this work is how to measure the degree of solidity of a closed convex cone in the Euclidean space ${\mathbb{R}^n}$ . One compares and establishes all sort of relations between the metric, the volumetric, and the Frobenius solidity indices.     

Generating the weakly efficient set of nonconvex multiobjective problems

We present a method for generating the set of weakly efficient solutions of a nonconvex multiobjective optimization problem. The convergence of the method is proven and some numerical examples are encountered.      

Saddle points and scalarizing sets in multiple objective linear programming

The main purpose of this paper is to study saddle points of the vector Lagrangian function associated with a multiple objective linear programming problem. We introduce three concepts of saddle points and establish their characterizations by solving suitable systems of equalities and inequalities. We deduce dual programs and prove a relationship between saddle points and dual solutions, which enables us to obtain an explicit expression of the scalarizing set of a given saddle point in terms of normal vectors to the value set of the problem. Finally, we present an algorithm to compute saddle points associated with non-degenerate vertices and the corresponding scalarizing sets.