We extend the work of Letchford (2000) by introducing a new class of valid inequalities for the traveling salesman problem, called the generalized domino-parity (GDP) constraints. Just as Letchford’s domino-parity constraints generalize comb inequalities, GDP constraints generalize the most well-known multiple-handle constraints, including clique-tree, bipartition, path, and star inequalities. ...

The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit ine...

The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit ine...

Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the BakryEmery curvature condition, the subordinate semigroup with power α satisfies a dimension-free Harnack inequality provided α ∈ ` 1 2 , 1 ́ , and it satisfies the log-Harnack inequality for all α ∈ (0, 1). Some infinite-dimensional examples are also presen...

This expository article shows how classical inequalities for the derivative of polynomials can be proved in real and complex Hilbert spaces using only elementary arguments from functional analysis. As we shall see, there is a surprising interconnection between an equality of norms for symmetric multilinear mappings due to Banach and an inequality for the derivative of trigonometric polynomials ...

Reprints available directly from the publisher Photocopying permitted by license only (C) 1999 OPA (Overseas Publishers Association) N.V. Let 0 <j < m _< n be integers. Denote by I1" the norm Ilfll f2 f2(x) exp(-x2) dx. For various positive values of A and B we establish Kolmogoroff type inequalities ilfU) < , Ill (m) + BIIfll AOk + B#k with certain constants Oke lZk, which hold for every fE 7r...

Embedded software in critical systems rise a need for software analysis, especially for guaranteeing safety properties. In the late seventies, Cousot & Cousot introduced a general framework, called abstract interpretation, dedicated to the conception of particular analyses: static analyses. Among the program properties of interest, discovering algebraic relationships between variables allows fo...

How can one find real solutions (x1, x2)? How to prove that they do not exist? And if the solution set is nonempty, how to optimize a polynomial function over this set? Until a few years ago, the default answer to these and similar questions would have been that the possi­ ble nonconvexity of the feasible set and/or objective function precludes any kind of analytic global results. Even today, t...

We prove that the Tutte polynomial of a coloopless paving matroid is convex along the portions of the line segments x + y = p lying in the positive quadrant. Every coloopless paving matroid is in the class of matroids which contain two disjoint bases or whose ground set is the union of two bases. For this latter class we give a proof that TM (a, a) ≤ max{TM (2a, 0), TM (0, 2a)} for a ≥ 2. We co...