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作者：Pataki, G
作者单位：Columbia University
摘要：We derive some basic results on the geometry of semidefinite programming (SDP) and eigenvalue-optimization, i.e., the minimization of the sum of the k largest eigenvalues of a smooth matrix-valued function. We provide upper bounds on the rank of extreme matrices in SDPs, and the first theoretically solid explanation of a phenomenon of intrinsic interest in eigenvalue-optimization. In the spectrum of an optimal matrix, the kth and (k + 1)st largest eigenvalues tend to be equal and frequently ha...
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作者：Naiman, DQ; Stone, RE
作者单位：Johns Hopkins University
摘要：A real square matrix M is said to be a e-matrix if the linear complementarity problem (q, M) has a solution for every vector q. There is, as yet, no characterization of e-matrices which makes it easy to determine whether or not a given matrix is Q. Ideas from topology, in particular degree theory, have previously been used to obtain sufficient conditions fdr when a matrix is Q. In this paper we will apply some other ideas from topology to give a homological characterization of Q-matrices. Cont...
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作者：Li, W; Singer, I
作者单位：Old Dominion University; Institute of Mathematics of the Romanian Academy; Romanian Academy
摘要：We give some results on the existence of global error bounds for convex multifunctions between normed linear spaces (until the present, only some results on local error bounds have been known in this general setting). As applications we obtain, among others, improvements of a theorem of Robinson on global error bounds for convex inequalities, of a result of Luo and Tseng on uniform boundedness of the Hoffman constants for linear inequalities and equalities, and of Lotov's result on pointwise L...
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作者：Coffman, EG; Puhalskii, AA; Reiman, MI
作者单位：Alcatel-Lucent; Lucent Technologies; AT&T; Russian Academy of Sciences
摘要：This paper studies the classical polling model under the exhaustive-service assumption; such models continue to be very useful in performance studies of computer/communication systems. The analysis here extends earlier work of the authors to the general case of nonzero switchover times. It shows that, under the standard heavy-traffic scaling, the total unfinished work in the system tends to a Bessel-type diffusion in the heavy-traffic limit. It verifies in addition that, with this change in th...
