66 research outputs found
Distributed Partitioned Big-Data Optimization via Asynchronous Dual Decomposition
In this paper we consider a novel partitioned framework for distributed
optimization in peer-to-peer networks. In several important applications the
agents of a network have to solve an optimization problem with two key
features: (i) the dimension of the decision variable depends on the network
size, and (ii) cost function and constraints have a sparsity structure related
to the communication graph. For this class of problems a straightforward
application of existing consensus methods would show two inefficiencies: poor
scalability and redundancy of shared information. We propose an asynchronous
distributed algorithm, based on dual decomposition and coordinate methods, to
solve partitioned optimization problems. We show that, by exploiting the
problem structure, the solution can be partitioned among the nodes, so that
each node just stores a local copy of a portion of the decision variable
(rather than a copy of the entire decision vector) and solves a small-scale
local problem
Decentralized Proximal Method of Multipliers for Convex Optimization with Coupled Constraints
In this paper, a decentralized proximal method of multipliers (DPMM) is
proposed to solve constrained convex optimization problems over multi-agent
networks, where the local objective of each agent is a general closed convex
function, and the constraints are coupled equalities and inequalities. This
algorithm strategically integrates the dual decomposition method and the
proximal point algorithm. One advantage of DPMM is that subproblems can be
solved inexactly and in parallel by agents at each iteration, which relaxes the
restriction of requiring exact solutions to subproblems in many distributed
constrained optimization algorithms. We show that the first-order optimality
residual of the proposed algorithm decays to at a rate of under
general convexity. Furthermore, if a structural assumption for the considered
optimization problem is satisfied, the sequence generated by DPMM converges
linearly to an optimal solution. In numerical simulations, we compare DPMM with
several existing algorithms using two examples to demonstrate its
effectiveness
Improved Dynamic Regret of Distributed Online Multiple Frank-Wolfe Convex Optimization
In this paper, we consider a distributed online convex optimization problem
over a time-varying multi-agent network. The goal of this network is to
minimize a global loss function through local computation and communication
with neighbors. To effectively handle the optimization problem with a
high-dimensional and structural constraint set, we develop a distributed online
multiple Frank-Wolfe algorithm to avoid the expensive computational cost of
projection operation. The dynamic regret bounds are established as
with the linear oracle number , which depends on the horizon (total iteration number) , the
function variation , and the tuning parameter . In particular,
when the prior knowledge of and is available, the bound can be
enhanced to . Moreover, we illustrate the significant
advantages of the multiple iteration technique and reveal a trade-off between
dynamic regret bound, computational cost, and communication cost. Finally, the
performance of our algorithm is verified and compared through the distributed
online ridge regression problems with two constraint sets
Resource management techniques for sustainable networks with energy harvesting nodes
Premi extraordinari doctorat UPC curs 2015-2016, Ã mbit Enginyeria de les TICThis dissertation proposes novel techniques for assigning resources of wireless networks by considering that the coverage radii are small, implying that some power consumption sinks not considered so far shouldnow be introduced, and by considering that the devices are battery-powered terminals provided with energy harvesting capabilities. In this framework, two different configurations in terms of harvesting capabilities are considered. First, we assume that the energy source is external and not controllable, e.g. solar energy. In this context, the proposed design should adapt to the energy that is currently being harvested. We also study the effect of having a finite backhaul connection that links the wireless access network with the core network. On the other hand, we propose a design in which the transmitter feeds actively the receivers with energy by transmitting signals that receivers use for recharging their batteries. In this case, the power transfer design should be carried out jointly with the power control strategy for users that receive information as both procedures, transfer of information and transfer of power, are implemented at the transmitter and make use of a common resource, i.e., power.
Apart from techniques for assigning the radio resources, this dissertation develops a procedure for switching on and off base stations. Concerning this, it is important to notice that the traffic profile is not constant throughout the day. This is precisely the feature that can be exploited to define a strategy based on a dynamic selection of the base stations to be switched off when the traffic load is low, without affecting the quality experienced by the users. Thanks to this procedure, we are able to deploy smaller energy harvesting sources and smaller batteries and, thus, to reduce the cost of the network deployment.
Finally, we derive some procedures to optimize high level decisions of the network operation in which variables from several layers of the protocol stack are involved. In this context, admission control procedures for deciding which user should be connected to which base station are studied, taking into account information of the average channel information, the current battery levels, etc. A multi-tier multi-cell scenario is assumed in which base stations belonging to different tiers have different capabilities, e.g., transmission power, battery size, end energy harvesting source size. A set of strategies that require different computational complexity are derived for scenarios with different user mobility requirements.Aquesta tesis doctoral proposa tècniques per assignar els recursos disponibles a les xarxes wireless considerant que els radis de cobertura són petits, el que implica que altres fonts de consum d’energia no considerades fins al moment s’hagin d’introduir dins els dissenys, i considerant que els dispositius estan alimentats amb bateries finites i que tenen a la seva disposició fonts de energy harvesting. En aquest context, es consideren dues configuracions diferents en funció de les capacitats de l’energia harvesting. En primer lloc, s’assumirà que la font d’energia és externa i incontrolable com, per exemple, l’energia solar. Els dissenys proposats han d’adaptar-se a l’energia que s’està recol·lectant en un precÃs moment. En segon lloc, es proposa un disseny en el qual el transmissor és capaç d’enviar energia als receptors mitjançant senyals de radiofreqüència dissenyats per aquest fi, energia que és utilitzada per recarregar les bateries. A part de tècniques d’assignació de recursos radio, en aquesta tesis doctoral es desenvolupa un procediment dinà mic per apagar i encendre estacions base. És important notar que el perfil de trà fic no és constant al llarg del dia. Aquest és precisament el patró que es pot explotar per definir una estratègia dinà mica per poder decidir quines estaciones base han de ser apagades, tot això sense afectar la qualitat experimentada pels usuaris. Grà cies a aquest procediment, es possible desplegar fonts d'energy harvesting més petites i bateries més petites. Finalment, aquesta tesis doctoral presenta procediments per optimitzar decisions de nivell més alt que afecten directament al funcionament global de la xarxa d’accés. Per prendre aquestes decisions, es fa ús de diverses variables que pertanyen a diferents capes de la pila de protocols. En aquest context, aquesta tesis aborda el disseny de tècniques de control d’admissió d’usuaris a estacions base en entorns amb múltiples estacions base, basant-se amb la informació estadÃstica dels canals, i el nivell actual de les bateries, entre altres. L'escenari considerat està format per múltiples estacions base, on cada estació base pertany a una famÃlia amb diferents capacitats, per exemple, potència de transmissió o mida de la bateria. Es deriven un conjunt de tècniques amb diferents costos computacionals que són d'utilitat per a poder aplicar a escenaris amb diferents mobilitats d’usuaris.Award-winningPostprint (published version
A Control-Theoretic Methodology for Adaptive Structured Parallel Computations
Adaptivity for distributed parallel applications is an essential feature whose impor- tance has been assessed in many research fields (e.g. scientific computations, large- scale real-time simulation systems and emergency management applications). Especially for high-performance computing, this feature is of special interest in order to properly and promptly respond to time-varying QoS requirements, to react to uncontrollable environ- mental effects influencing the underlying execution platform and to efficiently deal with highly irregular parallel problems. In this scenario the Structured Parallel Programming paradigm is a cornerstone for expressing adaptive parallel programs: the high-degree of composability of parallelization schemes, their QoS predictability formally expressed by performance models, are basic tools in order to introduce dynamic reconfiguration processes of adaptive applications. These reconfigurations are not only limited to imple- mentation aspects (e.g. parallelism degree modifications), but also parallel versions with different structures can be expressed for the same computation, featuring different levels of performance, memory utilization, energy consumption, and exploitation of the memory hierarchies.
Over the last decade several programming models and research frameworks have been developed aimed at the definition of tools and strategies for expressing adaptive parallel applications. Notwithstanding this notable research effort, properties like the optimal- ity of the application execution and the stability of control decisions are not sufficiently studied in the existing work. For this reason this thesis exploits a pioneer research in the context of providing formal theoretical tools founded on Control Theory and Game Theory techniques. Based on these approaches, we introduce a formal model for control- ling distributed parallel applications represented by computational graphs of structured parallelism schemes (also called skeleton-based parallelism).
Starting out from the performance predictability of structured parallelism schemes, in this thesis we provide a formalization of the concept of adaptive parallel module per- forming structured parallel computations. The module behavior is described in terms of a Hybrid System abstraction and reconfigurations are driven by a Predictive Control ap- proach. Experimental results show the effectiveness of this work, in terms of execution cost reduction as well as the stability degree of a system reconfiguration: i.e. how long a
reconfiguration choice is useful for targeting the required QoS levels.
This thesis also faces with the issue of controlling large-scale distributed applications composed of several interacting adaptive components. After a panoramic view of the existing control-theoretic approaches (e.g. based on decentralized, distributed or hierar- chical structures of controllers), we introduce a methodology for the distributed predictive control. For controlling computational graphs, the overall control problem consists in a set of coupled control sub-problems for each application module. The decomposition is- sue has a twofold nature: first of all we need to model the coupling relationships between control sub-problems, furthermore we need to introduce proper notions of negotiation and convergence in the control decisions collectively taken by the parallel modules of the application graph. This thesis provides a formalization through basic concepts of Non-cooperative Games and Cooperative Optimization. In the notable context of the dis- tributed control of performance and resource utilization, we exploit a formal description of the control problem providing results for equilibrium point existence and the compari- son of the control optimality with different adaptation strategies and interaction protocols. Discussions and a first validation of the proposed techniques are exploited through exper-
iments performed in a simulation environment
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization
Many real-life decision problems are discrete in nature. To solve such problems as mathematical optimization problems, integrality constraints are commonly incorporated in the model to reflect the choice of finitely many alternatives. At the same time, it is known that semidefinite programming is very suitable for obtaining strong relaxations of combinatorial optimization problems. In this dissertation, we study the interplay between semidefinite programming and integrality, where a special focus is put on the use of cutting-plane methods. Although the notions of integrality and cutting planes are well-studied in linear programming, integer semidefinite programs (ISDPs) are considered only recently. We show that manycombinatorial optimization problems can be modeled as ISDPs. Several theoretical concepts, such as the Chvátal-Gomory closure, total dual integrality and integer Lagrangian duality, are studied for the case of integer semidefinite programming. On the practical side, we introduce an improved branch-and-cut approach for ISDPs and a cutting-plane augmented Lagrangian method for solving semidefinite programs with a large number of cutting planes. Throughout the thesis, we apply our results to a wide range of combinatorial optimization problems, among which the quadratic cycle cover problem, the quadratic traveling salesman problem and the graph partition problem. Our approaches lead to novel, strong and efficient solution strategies for these problems, with the potential to be extended to other problem classes
A distributed control strategy for reactive power compensation in smart microgrids
We consider the problem of optimal reactive power compensation for the
minimization of power distribution losses in a smart microgrid. We first
propose an approximate model for the power distribution network, which allows
us to cast the problem into the class of convex quadratic, linearly
constrained, optimization problems. We then consider the specific problem of
commanding the microgenerators connected to the microgrid, in order to achieve
the optimal injection of reactive power. For this task, we design a randomized,
gossip-like optimization algorithm. We show how a distributed approach is
possible, where microgenerators need to have only a partial knowledge of the
problem parameters and of the state, and can perform only local measurements.
For the proposed algorithm, we provide conditions for convergence together with
an analytic characterization of the convergence speed. The analysis shows that,
in radial networks, the best performance can be achieved when we command
cooperation among units that are neighbors in the electric topology. Numerical
simulations are included to validate the proposed model and to confirm the
analytic results about the performance of the proposed algorithm
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