We present a framework for information inequalities, namely, inequalities involving only Shannon’s information measures, for discrete random variables. A region in IR2 1, denoted by , is identified to be the origin of all information inequalities involving n random variables in the sense that all such inequalities are partial characterizations of . A product from this framework is a simple calc...

The comb inequalities are a well-known class of facet-inducing inequalities for the Traveling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality...

Probabilistic inequalities for independent random variables and martingales play a prominent role in many different areas of mathematical research, such as harmonic analysis, probability theory, Banach space geometry and the study of symmetric function spaces. In the recent years, many of these classical probabilistic inequalities have been generalized to the context of noncommutative Lp-spaces...

In this paper, we use the Riemann-Liouville fractionalintegrals to establish some new integral inequalities related toChebyshev's functional in the case of two differentiable functions.

Ranks of subspaces of vector spaces satisfy all linear inequalities satisfied by entropies (including the standard Shannon inequalities) and an additional inequality due to Ingleton. It is known that the Shannon and Ingleton inequalities generate all such linear rank inequalities on up to four variables, but it has been an open question whether additional inequalities hold for the case of five ...

We investigate strong inequalities for mixed 0-1 integer programs derived from flow cover inequalities. Flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities. However, because of the sequential nature of the standard lifting techniques and the complexity of the optimization problems that have to be solved to obtain lifting coefficients, lif...

Path-block-cycle inequalities are valid, and sometimes facet-defining, inequalities for polytopes in connection with graph partitioning problems and corresponding multicut problems. Special cases of the inequalities were introduced by De Souza & Laurent (1995) and shown to be facet-defining for the equicut polytope. Generalizations of these inequalities were shown by Ferreira et al. (1996) to b...

Laurent & Poljak introduced a class of valid inequalities for the max-cut problem, called gap inequalities, which include many other known inequalities as special cases. The gap inequalities have received little attention and are poorly understood. This paper presents the first ever computational results. In particular, we start presenting a cuttingplane scheme based on an effective heuristic s...

We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. The inequalities exploit the submodularity of the binary restrictions and are based on the polymatroid inequalities over binaries for the diagonal case. We prove that the convex inequalities completely describe the convex hull of a single conic quadratic constraint as well as the rotated cone constraint ove...