Portfolio optimization should provide large benefits to investors, but standard mean-variance optimization (MVO) works so poorly in practice that optimization is often abandoned. The approaches developed to address this issue are often surrounded by mystique regarding how, why, and whether they...

In this paper we study the existence problem of a zero point of a function defined on a finite set of elements of the integer lattice Zn of the n-dimensional Euclidean space IRn. It is assumed that the set is integrally convex, which implies that the convex hull of the set can be subdivided in...

We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP), that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation dominates the one in the paper: D. Cvetkovic, M....

In this note we present both necessary and sufficient conditions for the existence of a linear static state feedback controller if the system is described by an index one descriptor system. A priori no definiteness restrictions are made w.r.t. the quadratic performance criterium. It is shown...

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} with the property that antipodal vertices on the...

In this note we consider the cooperative linear quadratic control problem. That is, the problem where a number of players, all facing a (different) linear quadratic control problem, decide to cooperate in order to optimize their performance.It is well-known, in case the performance criteria are...

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard...

In this note we consider the static output feedback linear quadratic control problem. We present both necessary and sufficient conditions under which this problem has a solution in case the involved cost depend only on the output and control variables. This result is used to present both...

The knapsack problem (KP) is concerned with the selection of a subset of multiple items with known positive values and weights such that the total value of selected items is maximized and their total weight does not exceed capacity. Item values, item weights, and capacity are known in the...