Interior points of the completely positive cone.

A matrix A is called completely positive if it can be decomposed as A = BB^T with an entrywise nonnegative matrix B. The set of all such matrices is a convex cone. We provide a characterization of the interior of this cone as well as of its dual

A Note on Nadir Values in Bicriteria Programming Problems

In multiple criteria programming, a decision maker has to choose a point from the set of efficient solutions. This is usually done by some interactive procedure, where he or she moves from one efficient point to the next until an acceptable solution has been reached. It is therefore important to provide some information about the "size" of the efficient set, i.e. to know the minimum (and maximum) criterion values over the efficient set. This is a difficult problem in general. In this paper, we show that for the bicriteria problem, the problem is easy. This does not only hold for the linear bicriteria problem, but also for more general problems. (author's abstract)Series: Forschungsberichte / Institut für Statisti

A Class of Problems where Dual Bounds Beat Underestimation Bounds

We investigate the problem of minimizing a nonconvex function with respect to convex constraints, and we study different techniques to compute a lower bound on the optimal value: The method of using convex envelope functions on one hand, and the method of exploiting nonconvex duality on the other hand. We investigate which technique gives the better bound and develop conditions under which the dual bound is strictly better than the convex envelope bound. As a byproduct, we derive some interesting results on nonconvex duality. (author's abstract)Series: Forschungsberichte / Institut für Statisti