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作者：Anstreicher, KM
作者单位：University of Iowa
摘要：We consider the volumetric barrier for semidefinite programming, or generalized volumetric barrier, as introduced by Nesterov and Nemirovskii. We extend several fundamental properties of the Volumetric barrier for a polyhedral set to the semidefinite case. Our analysis facilitates a simplified proof of self-concordance for the semidefinite volumetric barrier, as well as for the combined volumetric-logarithmic barrier for semidefinite programming. For both of these barriers we obtain self-conco...
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作者：Monteiro, RDC; Zanjácomo, PR
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Extending the previous work of Monteiro and Pang (1998), this paper studies properties of fundamental maps that can be used to describe the central path of the monotone nonlinear complementarity problems over the cone of symmetric positive semidefinite matrices. Instead of focusing our attention on a specific map as was done in the approach of Monteiro and Pang (1998), this paper considers a general form of a fundamental map and introduces conditions on the map that allow us to extend the main...
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作者：Aardal, K; Hurkens, CAJ; Lenstra, AK
作者单位：Utrecht University; Eindhoven University of Technology
摘要：We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction. It first rinds a short vector satisfying the system of diophantine equations, and a set of Vectors belonging to the null-space of the constraint matrix. Due to basis reduction, all these vectors are relatively short. The next step is to branch on linear combinations of the null-space vectors, which either yields a vector that sat...
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作者：Bonnans, JF; Haddou, M
作者单位：Inria; Universite de Orleans
摘要：This paper is devoted to the mathematical study of a routing problem in telecommunication networks, when the cost function is the average delay of communications. We establish asymptotic expansions for the Value function and solutions in the vicinity of a congested nominal problem. The study is strongly related to the one of a partial inverse barrier method for linear programming.
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作者：Molchanov, I; Zuyev, S
作者单位：University of Glasgow; University of Strathclyde
摘要：Let F(II) be a functional of a (generally nonhomogeneous) Poisson process II with intensity measure mu. Considering the expectation EmuF(II) as a functional of mu from the cone M of positive finite measures, we derive closed form expressions for its Frechet derivatives of an orders that generalize the perturbation analysis formulae for Poisson processes. Variational methods developed for the space mm allow us to obtain first and second order sufficient conditions for various types of constrain...
