30,533 research outputs found
On the Finite Time Convergence of Cyclic Coordinate Descent Methods
Cyclic coordinate descent is a classic optimization method that has witnessed
a resurgence of interest in machine learning. Reasons for this include its
simplicity, speed and stability, as well as its competitive performance on
regularized smooth optimization problems. Surprisingly, very little is
known about its finite time convergence behavior on these problems. Most
existing results either just prove convergence or provide asymptotic rates. We
fill this gap in the literature by proving convergence rates (where
is the iteration counter) for two variants of cyclic coordinate descent
under an isotonicity assumption. Our analysis proceeds by comparing the
objective values attained by the two variants with each other, as well as with
the gradient descent algorithm. We show that the iterates generated by the
cyclic coordinate descent methods remain better than those of gradient descent
uniformly over time.Comment: 20 page
Interior Point Decoding for Linear Vector Channels
In this paper, a novel decoding algorithm for low-density parity-check (LDPC)
codes based on convex optimization is presented. The decoding algorithm, called
interior point decoding, is designed for linear vector channels. The linear
vector channels include many practically important channels such as inter
symbol interference channels and partial response channels. It is shown that
the maximum likelihood decoding (MLD) rule for a linear vector channel can be
relaxed to a convex optimization problem, which is called a relaxed MLD
problem. The proposed decoding algorithm is based on a numerical optimization
technique so called interior point method with barrier function. Approximate
variations of the gradient descent and the Newton methods are used to solve the
convex optimization problem. In a decoding process of the proposed algorithm, a
search point always lies in the fundamental polytope defined based on a
low-density parity-check matrix. Compared with a convectional joint message
passing decoder, the proposed decoding algorithm achieves better BER
performance with less complexity in the case of partial response channels in
many cases.Comment: 18 pages, 17 figures, The paper has been submitted to IEEE
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