2,287 research outputs found
Solving variational inequalities defined on a domain with infinitely many linear constraints
We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed method
Slow Adaptive OFDMA Systems Through Chance Constrained Programming
Adaptive OFDMA has recently been recognized as a promising technique for
providing high spectral efficiency in future broadband wireless systems. The
research over the last decade on adaptive OFDMA systems has focused on adapting
the allocation of radio resources, such as subcarriers and power, to the
instantaneous channel conditions of all users. However, such "fast" adaptation
requires high computational complexity and excessive signaling overhead. This
hinders the deployment of adaptive OFDMA systems worldwide. This paper proposes
a slow adaptive OFDMA scheme, in which the subcarrier allocation is updated on
a much slower timescale than that of the fluctuation of instantaneous channel
conditions. Meanwhile, the data rate requirements of individual users are
accommodated on the fast timescale with high probability, thereby meeting the
requirements except occasional outage. Such an objective has a natural chance
constrained programming formulation, which is known to be intractable. To
circumvent this difficulty, we formulate safe tractable constraints for the
problem based on recent advances in chance constrained programming. We then
develop a polynomial-time algorithm for computing an optimal solution to the
reformulated problem. Our results show that the proposed slow adaptation scheme
drastically reduces both computational cost and control signaling overhead when
compared with the conventional fast adaptive OFDMA. Our work can be viewed as
an initial attempt to apply the chance constrained programming methodology to
wireless system designs. Given that most wireless systems can tolerate an
occasional dip in the quality of service, we hope that the proposed methodology
will find further applications in wireless communications
From Cutting Planes Algorithms to Compression Schemes and Active Learning
Cutting-plane methods are well-studied localization(and optimization)
algorithms. We show that they provide a natural framework to perform
machinelearning ---and not just to solve optimization problems posed by
machinelearning--- in addition to their intended optimization use. In
particular, theyallow one to learn sparse classifiers and provide good
compression schemes.Moreover, we show that very little effort is required to
turn them intoeffective active learning methods. This last property provides a
generic way todesign a whole family of active learning algorithms from existing
passivemethods. We present numerical simulations testifying of the relevance
ofcutting-plane methods for passive and active learning tasks.Comment: IJCNN 2015, Jul 2015, Killarney, Ireland. 2015,
\<http://www.ijcnn.org/\&g
An interior point method for solving semidefinite programs using cutting planes and weighted analytic centers
We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed
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