3,042 research outputs found
A Majorization-Minimization Approach to Design of Power Transmission Networks
We propose an optimization approach to design cost-effective electrical power
transmission networks. That is, we aim to select both the network structure and
the line conductances (line sizes) so as to optimize the trade-off between
network efficiency (low power dissipation within the transmission network) and
the cost to build the network. We begin with a convex optimization method based
on the paper ``Minimizing Effective Resistance of a Graph'' [Ghosh, Boyd \&
Saberi]. We show that this (DC) resistive network method can be adapted to the
context of AC power flow. However, that does not address the combinatorial
aspect of selecting network structure. We approach this problem as selecting a
subgraph within an over-complete network, posed as minimizing the (convex)
network power dissipation plus a non-convex cost on line conductances that
encourages sparse networks where many line conductances are set to zero. We
develop a heuristic approach to solve this non-convex optimization problem
using: (1) a continuation method to interpolate from the smooth, convex problem
to the (non-smooth, non-convex) combinatorial problem, (2) the
majorization-minimization algorithm to perform the necessary intermediate
smooth but non-convex optimization steps. Ultimately, this involves solving a
sequence of convex optimization problems in which we iteratively reweight a
linear cost on line conductances to fit the actual non-convex cost. Several
examples are presented which suggest that the overall method is a good
heuristic for network design. We also consider how to obtain sparse networks
that are still robust against failures of lines and/or generators.Comment: 8 pages, 3 figures. To appear in Proc. 49th IEEE Conference on
Decision and Control (CDC '10
Partitioning Relational Matrices of Similarities or Dissimilarities using the Value of Information
In this paper, we provide an approach to clustering relational matrices whose
entries correspond to either similarities or dissimilarities between objects.
Our approach is based on the value of information, a parameterized,
information-theoretic criterion that measures the change in costs associated
with changes in information. Optimizing the value of information yields a
deterministic annealing style of clustering with many benefits. For instance,
investigators avoid needing to a priori specify the number of clusters, as the
partitions naturally undergo phase changes, during the annealing process,
whereby the number of clusters changes in a data-driven fashion. The
global-best partition can also often be identified.Comment: Submitted to the IEEE International Conference on Acoustics, Speech,
and Signal Processing (ICASSP
On the Link between Gaussian Homotopy Continuation and Convex Envelopes
Abstract. The continuation method is a popular heuristic in computer vision for nonconvex optimization. The idea is to start from a simpli-fied problem and gradually deform it to the actual task while tracking the solution. It was first used in computer vision under the name of graduated nonconvexity. Since then, it has been utilized explicitly or im-plicitly in various applications. In fact, state-of-the-art optical flow and shape estimation rely on a form of continuation. Despite its empirical success, there is little theoretical understanding of this method. This work provides some novel insights into this technique. Specifically, there are many ways to choose the initial problem and many ways to progres-sively deform it to the original task. However, here we show that when this process is constructed by Gaussian smoothing, it is optimal in a specific sense. In fact, we prove that Gaussian smoothing emerges from the best affine approximation to Veseās nonlinear PDE. The latter PDE evolves any function to its convex envelope, hence providing the optimal convexification
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