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Seminar
Department of Systems Engineering and Engineering Management
The Chinese University of Hong Kong

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 ¡¡ ¡¡ ¡¡ Title : Optimal Spectrum Management: Complexity, Duality and Approximation ¡¡ ¡¡ ¡¡ Speaker : Prof. Shuzhong Zhang ¡¡ ¡¡ Department of Systems Engineering & Engineering Management ¡¡ ¡¡ The Chinese University of Hong Kong (Joint work with Zhi-Quan Luo) ¡¡ ¡¡ ¡¡ Date : April 13th, 2007 (Friday) ¡¡ ¡¡ ¡¡ Time : 4:30 p.m. - 5:30 p.m. ¡¡ ¡¡ ¡¡ Venue : Room 513 ¡¡ ¡¡ William M.W. Mong Engineering Building ¡¡ ¡¡ (Engineering Building Complex Phase 2) ¡¡ ¡¡ CUHK ¡¡ ¡¡ ¡¡

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Abstract:
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 We consider a class of nonconvex optimization problems arising from spectrum management in multiuser communication. For the discretized version of this problem, we characterize its computational complexity under various practical settings and study the structure of its global optimal solutions. It is shown that this discretized nonconvex optimization problem is NP-hard in general and has a positive duality gap. Surprisingly this duality gap disappears asymptotically as the size of discretization step decreases to zero, thanks to a hidden convexity that can be uncovered by the Lyapunov Theorem in functional analysis. Based on this asymptotic zero duality result and a Lagrangian dual relaxation, we present an approximation scheme to compute an $\epsilon$-optimal solution for the continuous version of the resource management problem.

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Biography:
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 Shuzhong Zhang obtained his Bsc degree from Department of Mathematics, Fudan University, in 1984, and his Ph.D. degree in 1991 from Tinbergen Institute, Erasmus University, The Netherlands. He is currently a full professor at Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong. Prior to this position, he served as a faculty member at Department of Econometrics, University of Groningen (1991 - 1993), and at Econometric Institute, Erasmus University Rotterdam (1993 - 1999). He received the Vice-Chancellor's Exemplary Teaching Award of The Chinese University of Hong Kong in 2001, and the SIAM Outstanding Paper prize in 2003. He currently serves on editorial board of Operations Research, SIAM Journal on Optimization, Optimization and Engineering, and Pacific Journal of Optimization. His research interests include conic optimization, robust optimization, randomization algorithms, and their applications in engineering, management, and economics.

************************* ALL ARE WELCOME ************************

 ¡¡ ¡¡ ¡¡ Enquiries : Bolin Ding or Jeffrey Xu Yu ¡¡ : Department of Systems Engineering and Engineering Management ¡¡ ¡¡ CUHK Website : http://www.se.cuhk.edu.hk/~seg5810 Email : seg5810@se.cuhk.edu.hk ¡¡ ¡¡ ¡¡

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