5,677 research outputs found
A unified framework for primal-dual methods in minimum cost network flow problems
"October 1982."Bibliography: p. 32.National Science Foundation Contract NSF/ECS 79-20834by Dimitri P. Bertsekas
Less is More: Real-time Failure Localization in Power Systems
Cascading failures in power systems exhibit non-local propagation patterns
which make the analysis and mitigation of failures difficult. In this work, we
propose a distributed control framework inspired by the recently proposed
concepts of unified controller and network tree-partition that offers strong
guarantees in both the mitigation and localization of cascading failures in
power systems. In this framework, the transmission network is partitioned into
several control areas which are connected in a tree structure, and the unified
controller is adopted by generators or controllable loads for fast timescale
disturbance response. After an initial failure, the proposed strategy always
prevents successive failures from happening, and regulates the system to the
desired steady state where the impact of initial failures are localized as much
as possible. For extreme failures that cannot be localized, the proposed
framework has a configurable design, that progressively involves and
coordinates more control areas for failure mitigation and, as a last resort,
imposes minimal load shedding. We compare the proposed control framework with
Automatic Generation Control (AGC) on the IEEE 118-bus test system. Simulation
results show that our novel framework greatly improves the system robustness in
terms of the N-1 security standard, and localizes the impact of initial
failures in majority of the load profiles that are examined. Moreover, the
proposed framework incurs significantly less load loss, if any, compared to
AGC, in all of our case studies
Network Flow Algorithms for Structured Sparsity
We consider a class of learning problems that involve a structured
sparsity-inducing norm defined as the sum of -norms over groups of
variables. Whereas a lot of effort has been put in developing fast optimization
methods when the groups are disjoint or embedded in a specific hierarchical
structure, we address here the case of general overlapping groups. To this end,
we show that the corresponding optimization problem is related to network flow
optimization. More precisely, the proximal problem associated with the norm we
consider is dual to a quadratic min-cost flow problem. We propose an efficient
procedure which computes its solution exactly in polynomial time. Our algorithm
scales up to millions of variables, and opens up a whole new range of
applications for structured sparse models. We present several experiments on
image and video data, demonstrating the applicability and scalability of our
approach for various problems.Comment: accepted for publication in Adv. Neural Information Processing
Systems, 201
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Convex and Network Flow Optimization for Structured Sparsity
We consider a class of learning problems regularized by a structured
sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over
groups of variables. Whereas much effort has been put in developing fast
optimization techniques when the groups are disjoint or embedded in a
hierarchy, we address here the case of general overlapping groups. To this end,
we present two different strategies: On the one hand, we show that the proximal
operator associated with a sum of l_infinity-norms can be computed exactly in
polynomial time by solving a quadratic min-cost flow problem, allowing the use
of accelerated proximal gradient methods. On the other hand, we use proximal
splitting techniques, and address an equivalent formulation with
non-overlapping groups, but in higher dimension and with additional
constraints. We propose efficient and scalable algorithms exploiting these two
strategies, which are significantly faster than alternative approaches. We
illustrate these methods with several problems such as CUR matrix
factorization, multi-task learning of tree-structured dictionaries, background
subtraction in video sequences, image denoising with wavelets, and topographic
dictionary learning of natural image patches.Comment: to appear in the Journal of Machine Learning Research (JMLR
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