The Equivalence of Several Basic Theorems for Subdifferentials

Several different basic tools are used for studying subdifferentials. They are a nonlocal fuzzy sum rule in (Borwein et al., 1996; Zhu, 1996), a multidirectional mean value theorem in (Clarke and Ledyaev, 1994; Clarke et al., 1998), local fuzzy sum rules in (Ioffe, 1984, 1990) and an extremal principle in (Kruger and Mordukhovich, 1980; Mordukhovich, 1976, 1980, 1994). We show that all these basic results are equivalent and discuss some interesting consequences of this equivalence.     

Pricing and distributed QoS control for elastic network traffic

We study a processor-sharing model in which users choose between a high- and a low-priority service, based on their utility functions and prices charged by the service provider. The latter aims at revenue maximization. The model is motivated by file transmissions in data networks with distributed congestion control.     

关于非负随机变量的几个矩不等式

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一类椭圆型变分不等式离散问题的迭代算法

根据一类椭圆型变分不等式离散问题所具有的非线性特征，提出了一种简明快速的迭代算法，该方法在解决障碍问题及流体润滑油膜破裂自然边值问题等工程应用问题时具有较高的效率。     

Randomized UMD Banach spaces and decoupling inequalities for stochastic integrals

In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.

     

Computational experience with general equilibrium problems

We report on computational experience with an implementation of three algorithms for the general economic equilibrium problem. As a result we get that the projection algorithm for variational inequalities increases the size of solvable models by a factor of 5–10 in comparison with the classical homotopy method. As a third approach we implemented a simulated annealing heuristic which might be suitable to estimate equilibria for very large models.Supported by the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).     

Kirwan-Novikov inequalities on a manifold with boundary

We extend the Novikov Morse-type inequalities for closed 1-forms in 2 directions. First, we consider manifolds with boundary. Second, we allow a very degenerate structure of the critical set of the form, assuming only that the form is non-degenerated in the sense of Kirwan. In particular, we obtain a generalization of a result of Floer about the usual Morse inequalities on a manifold with boundary. We also obtain an equivariant version of our inequalities.

Our proof is based on an application of the Witten deformation technique. The main novelty here is that we consider the neighborhood of the critical set as a manifold with a cylindrical end. This leads to a considerable simplification of the local analysis. In particular, we obtain a new analytic proof of the Morse-Bott inequalities on a closed manifold.

     

SDP diagonalizations and perspective cuts for a class of nonseparable MIQP

We present a new approach, requiring the solution of a SemiDefinite Program, for decomposing the Hessian of a nonseparable mixed-integer quadratic problem to permit using perspective cuts to improve its continuous relaxation bound. The new method favorably compares with a previously proposed one requiring a minimum eigenvalue computation.     

Marcinkiewicz–Zygmund inequalities

We study a generalization of the classical Marcinkiewicz–Zygmund inequalities. We relate this problem to the sampling sequences in the Paley–Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz–Zygmund inequalities.     

关于Gerber不等式的一个猜想

本文证明了陈计-单墫关于Ｇｅｒｂｅｒ不等式的一个猜想，作为其应用，导出了单形内一点到顶点的距离与到面的距离的两个不等式．