68,071 research outputs found
Continuous-time Proportional-Integral Distributed Optimization for Networked Systems
In this paper we explore the relationship between dual decomposition and the
consensus-based method for distributed optimization. The relationship is
developed by examining the similarities between the two approaches and their
relationship to gradient-based constrained optimization. By formulating each
algorithm in continuous-time, it is seen that both approaches use a gradient
method for optimization with one using a proportional control term and the
other using an integral control term to drive the system to the constraint set.
Therefore, a significant contribution of this paper is to combine these methods
to develop a continuous-time proportional-integral distributed optimization
method. Furthermore, we establish convergence using Lyapunov stability
techniques and utilizing properties from the network structure of the
multi-agent system.Comment: 23 Pages, submission to Journal of Control and Decision, under
review. Takes comments from previous review process into account. Reasons for
a continuous approach are given and minor technical details are remedied.
Largest revision is reformatting for the Journal of Control and Decisio
Mapping constrained optimization problems to quantum annealing with application to fault diagnosis
Current quantum annealing (QA) hardware suffers from practical limitations
such as finite temperature, sparse connectivity, small qubit numbers, and
control error. We propose new algorithms for mapping boolean constraint
satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In
particular we develop a new embedding algorithm for mapping a CSP onto a
hardware Ising model with a fixed sparse set of interactions, and propose two
new decomposition algorithms for solving problems too large to map directly
into hardware.
The mapping technique is locally-structured, as hardware compatible Ising
models are generated for each problem constraint, and variables appearing in
different constraints are chained together using ferromagnetic couplings. In
contrast, global embedding techniques generate a hardware independent Ising
model for all the constraints, and then use a minor-embedding algorithm to
generate a hardware compatible Ising model. We give an example of a class of
CSPs for which the scaling performance of D-Wave's QA hardware using the local
mapping technique is significantly better than global embedding.
We validate the approach by applying D-Wave's hardware to circuit-based
fault-diagnosis. For circuits that embed directly, we find that the hardware is
typically able to find all solutions from a min-fault diagnosis set of size N
using 1000N samples, using an annealing rate that is 25 times faster than a
leading SAT-based sampling method. Further, we apply decomposition algorithms
to find min-cardinality faults for circuits that are up to 5 times larger than
can be solved directly on current hardware.Comment: 22 pages, 4 figure
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
Deriving the Normalized Min-Sum Algorithm from Cooperative Optimization
The normalized min-sum algorithm can achieve near-optimal performance at
decoding LDPC codes. However, it is a critical question to understand the
mathematical principle underlying the algorithm. Traditionally, people thought
that the normalized min-sum algorithm is a good approximation to the
sum-product algorithm, the best known algorithm for decoding LDPC codes and
Turbo codes. This paper offers an alternative approach to understand the
normalized min-sum algorithm. The algorithm is derived directly from
cooperative optimization, a newly discovered general method for
global/combinatorial optimization. This approach provides us another
theoretical basis for the algorithm and offers new insights on its power and
limitation. It also gives us a general framework for designing new decoding
algorithms.Comment: Accepted by IEEE Information Theory Workshop, Chengdu, China, 200
Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints
This paper investigates the relation between sequential convex programming
(SCP) as, e.g., defined in [24] and DC (difference of two convex functions)
programming. We first present an SCP algorithm for solving nonlinear
optimization problems with DC constraints and prove its convergence. Then we
combine the proposed algorithm with a relaxation technique to handle
inconsistent linearizations. Numerical tests are performed to investigate the
behaviour of the class of algorithms.Comment: 18 pages, 1 figur
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