We present a new approach for gluing tours over certain tight, 3-edge cuts. Gluing cuts has been used in algorithms finding Hamilton cycles special graph classes and proving bounds 2-edge-connected subgraph problem, but not much was known this direction connected multigraphs. apply to the traveling salesman problem (TSP) case when objective function of subtour elimination relaxation is minimize...

A new approach to multispectral and hyperspectral image analysis is presented. This method, called convex cone analysis (CCA), is based on the fact that some physical quantities such as radiance are nonnegative. The vectors formed by discrete radiance spectra are linear combinations of nonnegative components, and they lie inside a nonnegative, convex region. The object of CCA is to find the bou...

We study the conditions under which a semigroup is obtained upon convex combinations of channels. In particular, we set Pauli and generalized find that mixing only semigroups can never produce semigroup. Counter-intuitively, for combination to yield semigroup, most input channels have be noninvertible.

Linear programming is a very powerful technique, applicable not only in optimization, but in combinatorial theory. For example, we will see that König’s theorem (Lecture 1,Theorem 2) is an instance of the principle of (integral) linear programming duality. In this section, we remind ourselves of the basic relevant concepts. Given a collection of vectors v1, v2, . . . .vm ∈ R their linear combin...

The order structure of the set of six operators connected with quadrature rules is established in the class of 3–convex functions. Convex combinations of these operators are studied and their error bounds for four times differentiable functions are given. In some cases they are obtained for less regular functions as in the classical results. Quadrature Rules, Inequalities and Error Bounds Szymo...

The classical problem of finding a point in the intersection of countably many closed and convex sets in a Hilbert space is considered. Extrapolated iterations of convex combinations of approximate projections onto subfamilies of sets are investigated to solve this problem. General hypotheses are made on the regularity of the sets and various strategies are considered to control the order in wh...

Recent papers [3,4,16] have introduced dual-mode MPC algorithms using a time-varying terminal cost and/or constraint. The advantage of these methods is the enlargement of the admissible set of initial states whithout sacrificing local optimality of the controller, but this comes at the cost of a higher computational complexity. This paper delivers two main contributions in this area. First, a n...