22,589 research outputs found
Global Solutions to Nonconvex Optimization of 4th-Order Polynomial and Log-Sum-Exp Functions
This paper presents a canonical dual approach for solving a nonconvex global
optimization problem governed by a sum of fourth-order polynomial and a
log-sum-exp function. Such a problem arises extensively in engineering and
sciences. Based on the canonical duality-triality theory, this nonconvex
problem is transformed to an equivalent dual problem, which can be solved
easily under certain conditions. We proved that both global minimizer and the
biggest local extrema of the primal problem can be obtained analytically from
the canonical dual solutions. As two special cases, a quartic polynomial
minimization and a minimax problem are discussed. Existence conditions are
derived, which can be used to classify easy and relative hard instances.
Applications are illustrated by several nonconvex and nonsmooth examples
Foreign Direct Investment in the United States: Interest Rate and Exchange Rate
David Y. Chen, Ph.D., is an associate professor, Department of Economics and Transportation/ Logistics. North Carolina A&T State University, Greensboro, NC 27411
A Bijection between Atomic Partitions and Unsplitable Partitions
In the study of the algebra of symmetric functions in
noncommutative variables, Bergeron and Zabrocki found a free generating set
consisting of power sum symmetric functions indexed by atomic partitions. On
the other hand, Bergeron, Reutenauer, Rosas, and Zabrocki studied another free
generating set of consisting of monomial symmetric functions
indexed by unsplitable partitions. Can and Sagan raised the question of finding
a bijection between atomic partitions and unsplitable partitions. In this
paper, we provide such a bijection.Comment: 6 page
Analysis and Design of Multiple-Antenna Cognitive Radios with Multiple Primary User Signals
We consider multiple-antenna signal detection of primary user transmission
signals by a secondary user receiver in cognitive radio networks. The optimal
detector is analyzed for the scenario where the number of primary user signals
is no less than the number of receive antennas at the secondary user. We first
derive exact expressions for the moments of the generalized likelihood ratio
test (GLRT) statistic, yielding approximations for the false alarm and
detection probabilities. We then show that the normalized GLRT statistic
converges in distribution to a Gaussian random variable when the number of
antennas and observations grow large at the same rate. Further, using results
from large random matrix theory, we derive expressions to compute the detection
probability without explicit knowledge of the channel, and then particularize
these expressions for two scenarios of practical interest: 1) a single primary
user sending spatially multiplexed signals, and 2) multiple spatially
distributed primary users. Our analytical results are finally used to obtain
simple design rules for the signal detection threshold.Comment: Revised version (14 pages). Change in titl
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