18,547 research outputs found
Certificates of infeasibility via nonsmooth optimization
An important aspect in the solution process of constraint satisfaction
problems is to identify exclusion boxes which are boxes that do not contain
feasible points. This paper presents a certificate of infeasibility for finding
such boxes by solving a linearly constrained nonsmooth optimization problem.
Furthermore, the constructed certificate can be used to enlarge an exclusion
box by solving a nonlinearly constrained nonsmooth optimization problem.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0802
Nonlinear Integer Programming
Research efforts of the past fifty years have led to a development of linear
integer programming as a mature discipline of mathematical optimization. Such a
level of maturity has not been reached when one considers nonlinear systems
subject to integrality requirements for the variables. This chapter is
dedicated to this topic.
The primary goal is a study of a simple version of general nonlinear integer
problems, where all constraints are still linear. Our focus is on the
computational complexity of the problem, which varies significantly with the
type of nonlinear objective function in combination with the underlying
combinatorial structure. Numerous boundary cases of complexity emerge, which
sometimes surprisingly lead even to polynomial time algorithms.
We also cover recent successful approaches for more general classes of
problems. Though no positive theoretical efficiency results are available, nor
are they likely to ever be available, these seem to be the currently most
successful and interesting approaches for solving practical problems.
It is our belief that the study of algorithms motivated by theoretical
considerations and those motivated by our desire to solve practical instances
should and do inform one another. So it is with this viewpoint that we present
the subject, and it is in this direction that we hope to spark further
research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G.
Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50
Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art
Surveys, Springer-Verlag, 2009, ISBN 354068274
UA-DETRAC: A New Benchmark and Protocol for Multi-Object Detection and Tracking
In recent years, numerous effective multi-object tracking (MOT) methods are
developed because of the wide range of applications. Existing performance
evaluations of MOT methods usually separate the object tracking step from the
object detection step by using the same fixed object detection results for
comparisons. In this work, we perform a comprehensive quantitative study on the
effects of object detection accuracy to the overall MOT performance, using the
new large-scale University at Albany DETection and tRACking (UA-DETRAC)
benchmark dataset. The UA-DETRAC benchmark dataset consists of 100 challenging
video sequences captured from real-world traffic scenes (over 140,000 frames
with rich annotations, including occlusion, weather, vehicle category,
truncation, and vehicle bounding boxes) for object detection, object tracking
and MOT system. We evaluate complete MOT systems constructed from combinations
of state-of-the-art object detection and object tracking methods. Our analysis
shows the complex effects of object detection accuracy on MOT system
performance. Based on these observations, we propose new evaluation tools and
metrics for MOT systems that consider both object detection and object tracking
for comprehensive analysis.Comment: 18 pages, 11 figures, accepted by CVI
Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control
This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York
A Complete N-body Model of the Old Open Cluster M67
The old open cluster M67 is an ideal testbed for current cluster evolution
models because of its dynamically evolved structure and rich stellar
populations that show clear signs of interaction between stellar, binary and
cluster evolution. Here we present the first truly direct N-body model for M67,
evolved from zero age to 4 Gyr taking full account of cluster dynamics as well
as stellar and binary evolution. Our preferred model starts with 12000 single
stars and 12000 binaries placed in a Galactic tidal field at 8.0 kpc from the
Galactic Centre. Our choices for the initial conditions and for the primordial
binary population are explained in detail. At 4 Gyr, the age of M67, the total
mass has reduced by 90% as a result of mass loss and stellar escapes. The mass
and half-mass radius of luminous stars in the cluster are a good match to
observations although the model is more centrally concentrated than
observations indicate. The stellar mass and luminosity functions are
significantly flattened by preferential escape of low-mass stars. We find that
M67 is dynamically old enough that information about the initial mass function
is lost, both from the current luminosity function and from the current mass
fraction in white dwarfs. The model contains 20 blue stragglers at 4 Gyr which
is slightly less than the 28 observed in M67. Nine are in binaries. The blue
stragglers were formed by a variety of means and we find formation paths for
the whole variety observed in M67. Both the primordial binary population and
the dynamical cluster environment play an essential role in shaping the
population. A substantial population of short-period primordial binaries (with
periods less than a few days) is needed to explain the observed number of blue
stragglers in M67.Comment: 32 pages, 17 figures, submitted to MNRA
A Complete Spectroscopic Survey of the Milky Way Satellite Segue 1: The Darkest Galaxy
We present the results of a comprehensive Keck/DEIMOS spectroscopic survey of
the ultra-faint Milky Way satellite galaxy Segue 1. We have obtained velocity
measurements for 98.2% of the stars within 67 pc (10 arcmin, or 2.3 half-light
radii) of the center of Segue 1 that have colors and magnitudes consistent with
membership, down to a magnitude limit of r=21.7. Based on photometric,
kinematic, and metallicity information, we identify 71 stars as probable Segue
1 members, including some as far out as 87 pc. After correcting for the
influence of binary stars using repeated velocity measurements, we determine a
velocity dispersion of 3.7^{+1.4}_{-1.1} km/s, with a corresponding mass within
the half-light radius of 5.8^{+8.2}_{-3.1} x 10^5 Msun. The stellar kinematics
of Segue 1 require very high mass-to-light ratios unless the system is far from
dynamical equilibrium, even if the period distribution of unresolved binary
stars is skewed toward implausibly short periods. With a total luminosity less
than that of a single bright red giant and a V-band mass-to-light ratio of 3400
Msun/Lsun, Segue 1 is the darkest galaxy currently known. We critically
re-examine recent claims that Segue 1 is a tidally disrupting star cluster and
that kinematic samples are contaminated by the Sagittarius stream. The
extremely low metallicities ([Fe/H] < -3) of two Segue 1 stars and the large
metallicity spread among the members demonstrate conclusively that Segue 1 is a
dwarf galaxy, and we find no evidence in favor of tidal effects. We also show
that contamination by the Sagittarius stream has been overestimated. Segue 1
has the highest measured dark matter density of any known galaxy and will
therefore be a prime testing ground for dark matter physics and galaxy
formation on small scales.Comment: 24 pages, 4 tables, 11 figures (10 in color). Submitted for
publication in ApJ. V3 revised according to comments from the refere
Asymmetries arising from the space-filling nature of vascular networks
Cardiovascular networks span the body by branching across many generations of
vessels. The resulting structure delivers blood over long distances to supply
all cells with oxygen via the relatively short-range process of diffusion at
the capillary level. The structural features of the network that accomplish
this density and ubiquity of capillaries are often called space-filling. There
are multiple strategies to fill a space, but some strategies do not lead to
biologically adaptive structures by requiring too much construction material or
space, delivering resources too slowly, or using too much power to move blood
through the system. We empirically measure the structure of real networks (18
humans and 1 mouse) and compare these observations with predictions of model
networks that are space-filling and constrained by a few guiding biological
principles. We devise a numerical method that enables the investigation of
space-filling strategies and determination of which biological principles
influence network structure. Optimization for only a single principle creates
unrealistic networks that represent an extreme limit of the possible structures
that could be observed in nature. We first study these extreme limits for two
competing principles, minimal total material and minimal path lengths. We
combine these two principles and enforce various thresholds for balance in the
network hierarchy, which provides a novel approach that highlights the
trade-offs faced by biological networks and yields predictions that better
match our empirical data.Comment: 17 pages, 15 figure
Discrete Optimization for Interpretable Study Populations and Randomization Inference in an Observational Study of Severe Sepsis Mortality
Motivated by an observational study of the effect of hospital ward versus
intensive care unit admission on severe sepsis mortality, we develop methods to
address two common problems in observational studies: (1) when there is a lack
of covariate overlap between the treated and control groups, how to define an
interpretable study population wherein inference can be conducted without
extrapolating with respect to important variables; and (2) how to use
randomization inference to form confidence intervals for the average treatment
effect with binary outcomes. Our solution to problem (1) incorporates existing
suggestions in the literature while yielding a study population that is easily
understood in terms of the covariates themselves, and can be solved using an
efficient branch-and-bound algorithm. We address problem (2) by solving a
linear integer program to utilize the worst case variance of the average
treatment effect among values for unobserved potential outcomes that are
compatible with the null hypothesis. Our analysis finds no evidence for a
difference between the sixty day mortality rates if all individuals were
admitted to the ICU and if all patients were admitted to the hospital ward
among less severely ill patients and among patients with cryptic septic shock.
We implement our methodology in R, providing scripts in the supplementary
material
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