5,264 research outputs found
Conjunctions of Among Constraints
Many existing global constraints can be encoded as a conjunction of among
constraints. An among constraint holds if the number of the variables in its
scope whose value belongs to a prespecified set, which we call its range, is
within some given bounds. It is known that domain filtering algorithms can
benefit from reasoning about the interaction of among constraints so that
values can be filtered out taking into consideration several among constraints
simultaneously. The present pa- per embarks into a systematic investigation on
the circumstances under which it is possible to obtain efficient and complete
domain filtering algorithms for conjunctions of among constraints. We start by
observing that restrictions on both the scope and the range of the among
constraints are necessary to obtain meaningful results. Then, we derive a
domain flow-based filtering algorithm and present several applications. In
particular, it is shown that the algorithm unifies and generalizes several
previous existing results.Comment: 15 pages plus appendi
On the Reification of Global Constraints
We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on
the observation that most global constraints can be reformulated as a conjunction of pure functional dependency
constraints together with a constraint that can be easily reified. We first show how the core constraints of the
Global Constraint Catalogue can be reified and we then identify several reification categories that apply to at
least 82% of the constraints in the Global Constraint Catalogue
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
The affine rank minimization problem consists of finding a matrix of minimum
rank that satisfies a given system of linear equality constraints. Such
problems have appeared in the literature of a diverse set of fields including
system identification and control, Euclidean embedding, and collaborative
filtering. Although specific instances can often be solved with specialized
algorithms, the general affine rank minimization problem is NP-hard. In this
paper, we show that if a certain restricted isometry property holds for the
linear transformation defining the constraints, the minimum rank solution can
be recovered by solving a convex optimization problem, namely the minimization
of the nuclear norm over the given affine space. We present several random
ensembles of equations where the restricted isometry property holds with
overwhelming probability. The techniques used in our analysis have strong
parallels in the compressed sensing framework. We discuss how affine rank
minimization generalizes this pre-existing concept and outline a dictionary
relating concepts from cardinality minimization to those of rank minimization
A track-before-detect labelled multi-Bernoulli particle filter with label switching
This paper presents a multitarget tracking particle filter (PF) for general
track-before-detect measurement models. The PF is presented in the random
finite set framework and uses a labelled multi-Bernoulli approximation. We also
present a label switching improvement algorithm based on Markov chain Monte
Carlo that is expected to increase filter performance if targets get in close
proximity for a sufficiently long time. The PF is tested in two challenging
numerical examples.Comment: Accepted for publication in IEEE Transactions on Aerospace and
Electronic System
A hybrid constraint programming and semidefinite programming approach for the stable set problem
This work presents a hybrid approach to solve the maximum stable set problem,
using constraint and semidefinite programming. The approach consists of two
steps: subproblem generation and subproblem solution. First we rank the
variable domain values, based on the solution of a semidefinite relaxation.
Using this ranking, we generate the most promising subproblems first, by
exploring a search tree using a limited discrepancy strategy. Then the
subproblems are being solved using a constraint programming solver. To
strengthen the semidefinite relaxation, we propose to infer additional
constraints from the discrepancy structure. Computational results show that the
semidefinite relaxation is very informative, since solutions of good quality
are found in the first subproblems, or optimality is proven immediately.Comment: 14 page
LQG Control and Sensing Co-Design
We investigate a Linear-Quadratic-Gaussian (LQG) control and sensing
co-design problem, where one jointly designs sensing and control policies. We
focus on the realistic case where the sensing design is selected among a finite
set of available sensors, where each sensor is associated with a different cost
(e.g., power consumption). We consider two dual problem instances:
sensing-constrained LQG control, where one maximizes control performance
subject to a sensor cost budget, and minimum-sensing LQG control, where one
minimizes sensor cost subject to performance constraints. We prove no
polynomial time algorithm guarantees across all problem instances a constant
approximation factor from the optimal. Nonetheless, we present the first
polynomial time algorithms with per-instance suboptimality guarantees. To this
end, we leverage a separation principle, that partially decouples the design of
sensing and control. Then, we frame LQG co-design as the optimization of
approximately supermodular set functions; we develop novel algorithms to solve
the problems; and we prove original results on the performance of the
algorithms, and establish connections between their suboptimality and
control-theoretic quantities. We conclude the paper by discussing two
applications, namely, sensing-constrained formation control and
resource-constrained robot navigation.Comment: Accepted to IEEE TAC. Includes contributions to submodular function
optimization literature, and extends conference paper arXiv:1709.0882
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