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A Complete Characterization of the Gap between Convexity and SOSConvexity
"... Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials via the definition of convexity, its first order characterization, and its second order characterization are equivalent. These three equivalent algebraic ..."
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Cited by 6 (0 self)
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,d = ˜ ΣCn,d if and only if n = 1 or d = 2 or (n, d) = (2, 4). We also present a complete characterization for forms (homogeneous polynomials) except for the case (n, d) = (3, 4) which is joint work with G. Blekherman and is to be published elsewhere. Our result states that the set Cn,d of convex forms
A convex polynomial that is not sosconvex
 Mathematical Programming
"... A multivariate polynomial p(x) = p(x1,...,xn) is sosconvex if its Hessian H(x) can be factored as H(x) = M T (x)M(x) with a possibly nonsquare polynomial matrix M(x). It is easy to see that sosconvexity is a sufficient condition for convexity of p(x). Moreover, the problem of deciding sosconvex ..."
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Cited by 17 (4 self)
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A multivariate polynomial p(x) = p(x1,...,xn) is sosconvex if its Hessian H(x) can be factored as H(x) = M T (x)M(x) with a possibly nonsquare polynomial matrix M(x). It is easy to see that sosconvexity is a sufficient condition for convexity of p(x). Moreover, the problem of deciding sosconvexity
Consensus and cooperation in networked multiagent systems
 PROCEEDINGS OF THE IEEE
"... This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An overview of ..."
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Cited by 772 (2 self)
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networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster
Wireless Communications
, 2005
"... Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University ..."
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Cited by 1129 (32 self)
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Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University
Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization
, 2000
"... ..."
Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms
 ACM TRANS. GRAPH
, 1990
"... This paper describes a generalpurpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur. T ..."
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Cited by 310 (19 self)
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This paper describes a generalpurpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur
The Convex Geometry of Linear Inverse Problems
, 2010
"... In applications throughout science and engineering one is often faced with the challenge of solving an illposed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constr ..."
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Cited by 181 (18 self)
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are constrained structurally so that they only have a few degrees of freedom relative to their ambient dimension. This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems
Sum Capacity of a Gaussian Vector Broadcast Channel
 IEEE Trans. Inform. Theory
, 2002
"... This paper characterizes the sum capacity of a class of nondegraded Gaussian vectB broadcast channels where a singletransmitter with multiple transmit terminals sends independent information to multiple receivers. Coordinat+[ is allowed among the transmit teminals, but not among the different recei ..."
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Cited by 280 (21 self)
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This paper characterizes the sum capacity of a class of nondegraded Gaussian vectB broadcast channels where a singletransmitter with multiple transmit terminals sends independent information to multiple receivers. Coordinat+[ is allowed among the transmit teminals, but not among the different
Putting Auction Theory to Work: The Simultaneous Ascending Auction
 Journal of Political Economy
, 2000
"... I review the uses of economic theory in the initial design and later improvement of the ‘‘simultaneous ascending auction,’ ’ which was developed initially for the sale of radio spectrum licenses in the United States. I analyze some capabilities and limitations of the auction, the roles of various de ..."
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Cited by 268 (21 self)
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I review the uses of economic theory in the initial design and later improvement of the ‘‘simultaneous ascending auction,’ ’ which was developed initially for the sale of radio spectrum licenses in the United States. I analyze some capabilities and limitations of the auction, the roles of various detailed rules, the possibilities for introducing combinatorial bidding, and some considerations in adapting the auction for sales in which revenue, rather than efficiency, is the primary goal. I.
Continuous Speech Recognition by Statistical Methods
 Proceedings of the IEEE 64
, 1976
"... HIS PAPER DESCRIBES statistical methods of automatic recognition (transcription) of continuous speech that have been used successfully by the Speech Processing Group at the IBM Thomas J. Watson Research Center. The ..."
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Cited by 243 (1 self)
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HIS PAPER DESCRIBES statistical methods of automatic recognition (transcription) of continuous speech that have been used successfully by the Speech Processing Group at the IBM Thomas J. Watson Research Center. The
Results 1  10
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