10,821 research outputs found
A path following algorithm for the graph matching problem
We propose a convex-concave programming approach for the labeled weighted
graph matching problem. The convex-concave programming formulation is obtained
by rewriting the weighted graph matching problem as a least-square problem on
the set of permutation matrices and relaxing it to two different optimization
problems: a quadratic convex and a quadratic concave optimization problem on
the set of doubly stochastic matrices. The concave relaxation has the same
global minimum as the initial graph matching problem, but the search for its
global minimum is also a hard combinatorial problem. We therefore construct an
approximation of the concave problem solution by following a solution path of a
convex-concave problem obtained by linear interpolation of the convex and
concave formulations, starting from the convex relaxation. This method allows
to easily integrate the information on graph label similarities into the
optimization problem, and therefore to perform labeled weighted graph matching.
The algorithm is compared with some of the best performing graph matching
methods on four datasets: simulated graphs, QAPLib, retina vessel images and
handwritten chinese characters. In all cases, the results are competitive with
the state-of-the-art.Comment: 23 pages, 13 figures,typo correction, new results in sections 4,5,
Optimal Universal Controllers for Roll Stabilization
Roll stabilization is an important problem of ship motion control. This
problem becomes especially difficult if the same set of actuators (e.g. a
single rudder) has to be used for roll stabilization and heading control of the
vessel, so that the roll stabilizing system interferes with the ship autopilot.
Finding the "trade-off" between the concurrent goals of accurate vessel
steering and roll stabilization usually reduces to an optimization problem,
which has to be solved in presence of an unknown wave disturbance. Standard
approaches to this problem (loop-shaping, LQG, -control etc.)
require to know the spectral density of the disturbance, considered to be a
\colored noise". In this paper, we propose a novel approach to optimal roll
stabilization, approximating the disturbance by a polyharmonic signal with
known frequencies yet uncertain amplitudes and phase shifts. Linear quadratic
optimization problems in presence of polyharmonic disturbances can be solved by
means of the theory of universal controllers developed by V.A. Yakubovich. An
optimal universal controller delivers the optimal solution for any uncertain
amplitudes and phases. Using Marine Systems Simulator (MSS) Toolbox that
provides a realistic vessel's model, we compare our design method with
classical approaches to optimal roll stabilization. Among three controllers
providing the same quality of yaw steering, OUC stabilizes the roll motion most
efficiently
Separable Convex Optimization with Nested Lower and Upper Constraints
We study a convex resource allocation problem in which lower and upper bounds
are imposed on partial sums of allocations. This model is linked to a large
range of applications, including production planning, speed optimization,
stratified sampling, support vector machines, portfolio management, and
telecommunications. We propose an efficient gradient-free divide-and-conquer
algorithm, which uses monotonicity arguments to generate valid bounds from the
recursive calls, and eliminate linking constraints based on the information
from sub-problems. This algorithm does not need strict convexity or
differentiability. It produces an -approximate solution for the
continuous problem in time
and an integer solution in time, where is
the number of decision variables, is the number of constraints, and is
the resource bound. A complexity of is also achieved
for the linear and quadratic cases. These are the best complexities known to
date for this important problem class. Our experimental analyses confirm the
good performance of the method, which produces optimal solutions for problems
with up to 1,000,000 variables in a few seconds. Promising applications to the
support vector ordinal regression problem are also investigated
Graph-Search and Differential Equations for Time-Optimal Vessel Route Planning in Dynamic Ocean Waves
Time-optimal paths are evaluated by VISIR (\u201cdis- coVerIng Safe and effIcient Routes\u201d), a graph-search ship routing model, with respect to the solution of the fundamental differential equations governing optimal paths in a dynamic wind-wave environment. The evaluation exercise makes use of identical setups: topological constraints, dynamic wave environmental conditions, and vessel-ocean parametrizations, while advection by external currents is not considered. The emphasis is on predicting the time-optimal ship headings and Speeds Through Water constrained by dynamic ocean wave fields. VISIR upgrades regarding angular resolution, time-interpolation, and static nav- igational safety constraints are introduced. The deviations of the graph-search results relative to the solution of the exact differential equations in both the path duration and length are assessed. They are found to be of the order of the discretization errors, with VISIR\u2019s solution converging to that of the differential equation for sufficient resolution
Adaptive Path Planning for Depth Constrained Bathymetric Mapping with an Autonomous Surface Vessel
This paper describes the design, implementation and testing of a suite of
algorithms to enable depth constrained autonomous bathymetric (underwater
topography) mapping by an Autonomous Surface Vessel (ASV). Given a target depth
and a bounding polygon, the ASV will find and follow the intersection of the
bounding polygon and the depth contour as modeled online with a Gaussian
Process (GP). This intersection, once mapped, will then be used as a boundary
within which a path will be planned for coverage to build a map of the
Bathymetry. Methods for sequential updates to GP's are described allowing
online fitting, prediction and hyper-parameter optimisation on a small embedded
PC. New algorithms are introduced for the partitioning of convex polygons to
allow efficient path planning for coverage. These algorithms are tested both in
simulation and in the field with a small twin hull differential thrust vessel
built for the task.Comment: 21 pages, 9 Figures, 1 Table. Submitted to The Journal of Field
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