161,997 research outputs found
Separable Convex Optimization with Nested Lower and Upper Constraints
We study a convex resource allocation problem in which lower and upper bounds
are imposed on partial sums of allocations. This model is linked to a large
range of applications, including production planning, speed optimization,
stratified sampling, support vector machines, portfolio management, and
telecommunications. We propose an efficient gradient-free divide-and-conquer
algorithm, which uses monotonicity arguments to generate valid bounds from the
recursive calls, and eliminate linking constraints based on the information
from sub-problems. This algorithm does not need strict convexity or
differentiability. It produces an -approximate solution for the
continuous problem in time
and an integer solution in time, where is
the number of decision variables, is the number of constraints, and is
the resource bound. A complexity of is also achieved
for the linear and quadratic cases. These are the best complexities known to
date for this important problem class. Our experimental analyses confirm the
good performance of the method, which produces optimal solutions for problems
with up to 1,000,000 variables in a few seconds. Promising applications to the
support vector ordinal regression problem are also investigated
Optimal experiment design in a filtering context with application to sampled network data
We examine the problem of optimal design in the context of filtering multiple
random walks. Specifically, we define the steady state E-optimal design
criterion and show that the underlying optimization problem leads to a second
order cone program. The developed methodology is applied to tracking network
flow volumes using sampled data, where the design variable corresponds to
controlling the sampling rate. The optimal design is numerically compared to a
myopic and a naive strategy. Finally, we relate our work to the general problem
of steady state optimal design for state space models.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS283 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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