10,291 research outputs found
Adapting the interior point method for the solution of linear programs on high performance computers
In this paper we describe a unified algorithmic framework for the interior point method (IPM) of solving Linear Programs (LPs) which allows us to adapt it over a range of high performance computer architectures. We set out the reasons as to why IPM makes better use of high performance computer architecture than the sparse simplex method. In the inner iteration of the IPM a search direction is computed using Newton or higher order methods. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system and the design of data structures to take advantage of coarse grain parallel and massively parallel computer architectures are considered in detail. Finally, we present experimental results of solving NETLIB test problems on examples of these architectures and put forward arguments as to why integration of the system within sparse simplex is beneficial
Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis
We propose a strategy for approximating Pareto optimal sets based on the
global analysis framework proposed by Smale (Dynamical systems, New York, 1973,
pp. 531-544). The method highlights and exploits the underlying manifold
structure of the Pareto sets, approximating Pareto optima by means of
simplicial complexes. The method distinguishes the hierarchy between singular
set, Pareto critical set and stable Pareto critical set, and can handle the
problem of superposition of local Pareto fronts, occurring in the general
nonconvex case. Furthermore, a quadratic convergence result in a suitable
set-wise sense is proven and tested in a number of numerical examples.Comment: 29 pages, 12 figure
Approximate Sparse Recovery: Optimizing Time and Measurements
An approximate sparse recovery system consists of parameters , an
-by- measurement matrix, , and a decoding algorithm, .
Given a vector, , the system approximates by , which must satisfy , where denotes the optimal -term approximation to . For
each vector , the system must succeed with probability at least 3/4. Among
the goals in designing such systems are minimizing the number of
measurements and the runtime of the decoding algorithm, .
In this paper, we give a system with
measurements--matching a lower bound, up to a constant factor--and decoding
time , matching a lower bound up to factors.
We also consider the encode time (i.e., the time to multiply by ),
the time to update measurements (i.e., the time to multiply by a
1-sparse ), and the robustness and stability of the algorithm (adding noise
before and after the measurements). Our encode and update times are optimal up
to factors
On-Manifold Preintegration for Real-Time Visual-Inertial Odometry
Current approaches for visual-inertial odometry (VIO) are able to attain
highly accurate state estimation via nonlinear optimization. However, real-time
optimization quickly becomes infeasible as the trajectory grows over time, this
problem is further emphasized by the fact that inertial measurements come at
high rate, hence leading to fast growth of the number of variables in the
optimization. In this paper, we address this issue by preintegrating inertial
measurements between selected keyframes into single relative motion
constraints. Our first contribution is a \emph{preintegration theory} that
properly addresses the manifold structure of the rotation group. We formally
discuss the generative measurement model as well as the nature of the rotation
noise and derive the expression for the \emph{maximum a posteriori} state
estimator. Our theoretical development enables the computation of all necessary
Jacobians for the optimization and a-posteriori bias correction in analytic
form. The second contribution is to show that the preintegrated IMU model can
be seamlessly integrated into a visual-inertial pipeline under the unifying
framework of factor graphs. This enables the application of
incremental-smoothing algorithms and the use of a \emph{structureless} model
for visual measurements, which avoids optimizing over the 3D points, further
accelerating the computation. We perform an extensive evaluation of our
monocular \VIO pipeline on real and simulated datasets. The results confirm
that our modelling effort leads to accurate state estimation in real-time,
outperforming state-of-the-art approaches.Comment: 20 pages, 24 figures, accepted for publication in IEEE Transactions
on Robotics (TRO) 201
LINVIEW: Incremental View Maintenance for Complex Analytical Queries
Many analytics tasks and machine learning problems can be naturally expressed
by iterative linear algebra programs. In this paper, we study the incremental
view maintenance problem for such complex analytical queries. We develop a
framework, called LINVIEW, for capturing deltas of linear algebra programs and
understanding their computational cost. Linear algebra operations tend to cause
an avalanche effect where even very local changes to the input matrices spread
out and infect all of the intermediate results and the final view, causing
incremental view maintenance to lose its performance benefit over
re-evaluation. We develop techniques based on matrix factorizations to contain
such epidemics of change. As a consequence, our techniques make incremental
view maintenance of linear algebra practical and usually substantially cheaper
than re-evaluation. We show, both analytically and experimentally, the
usefulness of these techniques when applied to standard analytics tasks. Our
evaluation demonstrates the efficiency of LINVIEW in generating parallel
incremental programs that outperform re-evaluation techniques by more than an
order of magnitude.Comment: 14 pages, SIGMO
MPI-Vector-IO: Parallel I/O and Partitioning for Geospatial Vector Data
In recent times, geospatial datasets are growing in terms of size, complexity and heterogeneity. High performance systems are needed to analyze such data to produce actionable insights in an efficient manner. For polygonal a.k.a vector datasets, operations such as I/O, data partitioning, communication, and load balancing becomes challenging in a cluster environment. In this work, we present MPI-Vector-IO 1 , a parallel I/O library that we have designed using MPI-IO specifically for partitioning and reading irregular vector data formats such as Well Known Text. It makes MPI aware of spatial data, spatial primitives and provides support for spatial data types embedded within collective computation and communication using MPI message-passing library. These abstractions along with parallel I/O support are useful for parallel Geographic Information System (GIS) application development on HPC platforms
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