In this survey we attempt to give a unified presentation of a variety of results on the lifting of valid inequalities, as well as a standard procedure combining mixed integer rounding with lifting for the development of strong valid inequalities for knapsack and single node flow sets. Our hope is that the latter can be used in practice to generate cutting planes for mixed integer programs. The ...

We explore the optimality of constants making valid recently established little Grothendieck inequality for JB$^*$-triples and JB$^*$-algebras. In our main result we prove that each bounded linear operator $T$ from a JB$^*$-algebra $B$ into

i ii Chapter 1 Introduction In [11], Hamilton determined a sharp differential Harnack inequality of Li–Yau type for complete solutions of the Ricci flow with non-negative curvature operator. This Li–Yau–Hamilton inequality (abbreviated as LYH inequality below) is of critical importance to the understanding of singularities of the Ricci flow, as is evident from its numerous applications in [10],...

Semidefinite programming has been used successfully to build hierarchies of convex relaxations to approximate polynomial programs. This approach rapidly becomes computationally expensive and is often tractable only for problems of small sizes. We propose an iterative scheme that improves the semidefinite relaxations without incurring exponential growth in their size. The key ingredient is a dyn...

In this paper we consider a new analytic center cutting plane method in a projective space. We prove the eeciency estimates for the general scheme and show that these results can be used in the analysis of a feasibility problem, the variational inequality problem and the problem of constrained minimization. Our analysis is valid even for the problems whose solution belongs to the boundary of th...

A sequence (xn)n 0 of positive real numbers is log-convex if the inequality xn xn−1xn+1 is valid for all n 1 . We show here how the problem of establishing the log-convexity of a given combinatorial sequence can be reduced to examining the ordinary convexity of related sequences. The new method is then used to prove that the sequence of Motzkin numbers is log-convex.

This note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the Stiefel manifold in terms of the expected norm of a standard Gaussian matrix with the same dimensions. A related comparison holds for any convex function of a random matrix drawn from the Stiefel manifold. For certain norms, a reversed inequality is also valid. Mathematics ...

We present dimension-free reverse Hölder inequalities for strong Ap weights, 1 ≤ p < ∞. We also provide a proof for the full range of local integrability of A1 weights. The common ingredient is a multidimensional version of Riesz’s “rising sun” lemma. Our results are valid for any nonnegative Radon measure with no atoms. For p =∞, we also provide a reverse Hölder inequality for certain product ...

From a sum rule for backward up scattering, valid only in the limit of large four-momentum transfer q2, we obtain an inequality for backward e-p inelastic scattering which depends ,upon the commutator of space components of isospin currents. Given chiral U(6) X U(6) current algebra, the total backward scattering at fixed large q2. is predicted to be at least as great as that from a point Dirac ...

Reenements of Sanov's large deviations theorem lead via Csiszz ar's information theoretic identity to reenements of the Gibbs conditioning principle which are valid for blocks whose length increase with the length of the conditioning sequence. Sharp bounds on the growth of the block length with the length of the conditioning sequence are derived. Extensions of Csiszz ar's triangle inequality an...