881 research outputs found
The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
Among various algorithms designed to exploit the specific properties of
quantum computers with respect to classical ones, the quantum adiabatic
algorithm is a versatile proposition to find the minimal value of an arbitrary
cost function (ground state energy). Random optimization problems provide a
natural testbed to compare its efficiency with that of classical algorithms.
These problems correspond to mean field spin glasses that have been extensively
studied in the classical case. This paper reviews recent analytical works that
extended these studies to incorporate the effect of quantum fluctuations, and
presents also some original results in this direction.Comment: 151 pages, 21 figure
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
New algorithmic developments in maximum consensus robust fitting
In many computer vision applications, the task of robustly estimating the set of parameters of
a geometric model is a fundamental problem. Despite the longstanding research efforts on robust
model fitting, there remains significant scope for investigation. For a large number of geometric
estimation tasks in computer vision, maximum consensus is the most popular robust fitting
criterion. This thesis makes several contributions in the algorithms for consensus maximization.
Randomized hypothesize-and-verify algorithms are arguably the most widely used class of
techniques for robust estimation thanks to their simplicity. Though efficient, these randomized
heuristic methods do not guarantee finding good maximum consensus estimates. To improve the
randomize algorithms, guided sampling approaches have been developed. These methods take
advantage of additional domain information, such as descriptor matching scores, to guide the
sampling process. Subsets of the data that are more likely to result in good estimates are prioritized
for consideration. However, these guided sampling approaches are ineffective when good
domain information is not available. This thesis tackles this shortcoming by proposing a new
guided sampling algorithm, which is based on the class of LP-type problems and Monte Carlo
Tree Search (MCTS). The proposed algorithm relies on a fundamental geometric arrangement
of the data to guide the sampling process. Specifically, we take advantage of the underlying tree
structure of the maximum consensus problem and apply MCTS to efficiently search the tree.
Empirical results show that the new guided sampling strategy outperforms traditional randomized
methods.
Consensus maximization also plays a key role in robust point set registration. A special case
is the registration of deformable shapes. If the surfaces have the same intrinsic shapes, their
deformations can be described accurately by a conformal model. The uniformization theorem
allows the shapes to be conformally mapped onto a canonical domain, wherein the shapes can be
aligned using a M¨obius transformation. The problem of correspondence-free M¨obius alignment
of two sets of noisy and partially overlapping point sets can be tackled as a maximum consensus
problem. Solving for the M¨obius transformation can be approached by randomized voting-type
methods which offers no guarantee of optimality. Local methods such as Iterative Closest Point
can be applied, but with the assumption that a good initialization is given or these techniques
may converge to a bad local minima. When a globally optimal solution is required, the literature
has so far considered only brute-force search. This thesis contributes a new branch-and-bound
algorithm that solves for the globally optimal M¨obius transformation much more efficiently.
So far, the consensus maximization problems are approached mainly by randomized algorithms,
which are efficient but offer no analytical convergence guarantee. On the other hand,
there exist exact algorithms that can solve the problem up to global optimality. The global methods,
however, are intractable in general due to the NP-hardness of the consensus maximization. To fill the gap between the two extremes, this thesis contributes two novel deterministic algorithms
to approximately optimize the maximum consensus criterion. The first method is based
on non-smooth penalization supported by a Frank-Wolfe-style optimization scheme, and another
algorithm is based on Alternating Direction Method of Multipliers (ADMM). Both of the
proposed methods are capable of handling the non-linear geometric residuals commonly used in
computer vision. As will be demonstrated, our proposed methods consistently outperform other
heuristics and approximate methods.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Computer Science, 201
CONSENSUS, PREDICTION AND OPTIMIZATION IN DIRECTED NETWORKS
This dissertation develops theory and algorithms for distributed consensus in multi-agent networks. The models considered are opinion dynamics models based on the well known DeGroot model. We study the following three related topics: consensus of networks with leaders, consensus prediction, and distributed optimization.
First, we revisit the problem of agreement seeking in a weighted directed network in the presence of leaders. We develop new sufficient conditions that are weaker than existing conditions for guaranteeing consensus for both fixed and switching network topologies, emphasizing the importance not only of persistent connectivity between the leader and the followers but also of the strength of the connections. We then study the problem of a leader aiming to maximize its influence on the opinions of the network agents through targeted connection with a limited number of agents, possibly in the presence of another leader having a competing opinion. We reveal fundamental properties of leader influence defined in terms of either the transient behavior or the achieved steady state opinions of the network agents. In particular, not only is the degree of this influence a supermodular set function, but its continuous relaxation is also convex for any strongly connected directed network. These results pave the way for developing efficient approximation algorithms admitting certain quality certifications, which when combined can provide effective tools and better analysis for optimal influence spreading in large networks.
Second, we introduce and investigate problems of network monitoring and consensus prediction. Here, an observer, without exact knowledge of the network, seeks to determine in the shortest possible time the asymptotic agreement value by monitoring a subset of the agents. We uncover a fundamental limit on the minimum required monitoring time for the case of a single observed node, and analyze the case of multiple observed nodes. We provide conditions for achieving the limit in the former case and develop algorithms toward achieving conjectured bounds in the latter through local observation and local computation.
Third, we study a distributed optimization problem where a network of agents seeks to minimize the sum of the agents' individual objective functions while each agent may be associated with a separate local constraint. We develop new distributed algorithms for solving this problem. In these algorithms, consensus prediction is employed as a means to achieve fast convergence rates, possibly in finite time. An advantage of our distributed optimization algorithms is that they work under milder assumptions on the network weight matrix than are commonly assumed in the literature. Most distributed algorithms require undirected networks. Consensus-based algorithms can apply to directed networks under an assumption that the network weight matrix is doubly stochastic (i.e., both row stochastic and column stochastic), or in some recent literature only column stochastic. Our algorithms work for directed networks and only require row stochasticity, a mild assumption. Doubly stochastic or column stochastic weight matrices can be hard to arrange locally, especially in broadcast-based communication. We achieve the simplification to the row stochastic assumption through a distributed rescaling technique. Next, we develop a unified convergence analysis of a distributed projected subgradient algorithm and its variation that can be applied to both unconstrained and constrained problems without assuming boundedness or commonality of the local constraint sets
A survey of outlier detection methodologies
Outlier detection has been used for centuries to detect and, where appropriate, remove anomalous observations from data. Outliers arise due to mechanical faults, changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. Their detection can identify system faults and fraud before they escalate with potentially catastrophic consequences. It can identify errors and remove their contaminating effect on the data set and as such to purify the data for processing. The original outlier detection methods were arbitrary but now, principled and systematic techniques are used, drawn from the full gamut of Computer Science and Statistics. In this paper, we introduce a survey of contemporary techniques for outlier detection. We identify their respective motivations and distinguish their advantages and disadvantages in a comparative review
Structure Exploitation in Mixed-Integer Optimization with Applications to Energy Systems
Das Ziel dieser Arbeit ist neue numerische Methoden für gemischt-ganzzahlige Optimierungsprobleme zu entwickeln um eine verbesserte Geschwindigkeit und Skalierbarkeit zu erreichen. Dies erfolgt durch Ausnutzung gängiger Problemstrukturen wie separierbarkeit oder Turnpike-eigenschaften. Methoden, die diese Strukturen ausnutzen können, wurden bereits im Bereich der verteilten Optimierung und optimalen Steuerung entwickelt, sie sind jedoch nicht direkt auf gemischt-ganztägige Probleme anwendbar.
Um verteilte Rechenressourcen zur Lösung von gemischt-ganzzahligen Problemen nutzen zu können, sind neue Methoden erforderlich. Zu diesem Zweck werden verschiedene Erweiterungen bestehender Methoden sowie neuartige Techniken zur gemischt-ganzzahligen Optimierung vorgestellt.
Benchmark-Probleme aus Strom- und Energiesystemen werden verwendet, um zu demonstrieren, dass die vorgestellten Methoden zu schnelleren Laufzeiten führen und die Lösung großer Probleme ermöglichen, die sonst nicht zentral gelöst werden können. Die vorliegende Arbeit enthält die folgenden Beiträge:
- Eine Erweiterung des Augmented Lagrangian Alternating Direction Inexact Newton-Algorithmus zur verteilten Optimierung für gemischt-ganzzahlige Probleme.
- Ein neuer, teilweise-verteilter Optimierungsalgorithmus für die gemischt-ganzzahlige Optimierung basierend auf äußeren Approximationsverfahren.
- Ein neuer Optimierungsalgorithmus für die verteilte gemischt-ganzzahlige Optimierung, der auf branch-and-bound Verfahren basiert.
- Eine erste Untersuchung von Turnpike-Eigenschaften bei Optimalsteuerungsproblemen mit gemischten-Ganzzahligen Entscheidungsgrößen und ein spezieller Algorithmus zur Lösung dieser Probleme.
- Eine neue Branch-and-Bound Heuristik, die a priori Probleminformationen effizienter nutzt als aktuelle Warmstarttechniken.
Schließlich wird gezeigt, dass die Ergebnisse der vorgestellten Optimierungsalgorithmen für verteilte gemischt-ganzzahlige Optimierung stark Partitionierungsabhängig sind. Zu diesem Zweck wird auch eine Untersuchung von Partitionierungsmethoden für die verteilte Optimierung vorgestellt
Systems Structure and Control
The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc
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