11,993 research outputs found
A Geometric relaxation solver for parametric constraint-based models
In this paper, a new relaxation algorithm for solving geometric
constraint-based models is proposed. The algorithm starts from a
constructive symbolic representation of objects (Constructive
Parametric Solid Model, CPSM) and proceeds by iterative relaxation of
the geometric constraints. Models that can be reduced to distance
and angle constraints can be handled. A new algorithm based on an
iterative global deformation of the system is presented and
discussed, and its convergence is proved. The performance of hybrid
algorithms involving global deformation and individual constraint
relaxation is discussed on several practical cases.Postprint (published version
Multi-Image Semantic Matching by Mining Consistent Features
This work proposes a multi-image matching method to estimate semantic
correspondences across multiple images. In contrast to the previous methods
that optimize all pairwise correspondences, the proposed method identifies and
matches only a sparse set of reliable features in the image collection. In this
way, the proposed method is able to prune nonrepeatable features and also
highly scalable to handle thousands of images. We additionally propose a
low-rank constraint to ensure the geometric consistency of feature
correspondences over the whole image collection. Besides the competitive
performance on multi-graph matching and semantic flow benchmarks, we also
demonstrate the applicability of the proposed method for reconstructing
object-class models and discovering object-class landmarks from images without
using any annotation.Comment: CVPR 201
Maximum Margin Clustering for State Decomposition of Metastable Systems
When studying a metastable dynamical system, a prime concern is how to
decompose the phase space into a set of metastable states. Unfortunately, the
metastable state decomposition based on simulation or experimental data is
still a challenge. The most popular and simplest approach is geometric
clustering which is developed based on the classical clustering technique.
However, the prerequisites of this approach are: (1) data are obtained from
simulations or experiments which are in global equilibrium and (2) the
coordinate system is appropriately selected. Recently, the kinetic clustering
approach based on phase space discretization and transition probability
estimation has drawn much attention due to its applicability to more general
cases, but the choice of discretization policy is a difficult task. In this
paper, a new decomposition method designated as maximum margin metastable
clustering is proposed, which converts the problem of metastable state
decomposition to a semi-supervised learning problem so that the large margin
technique can be utilized to search for the optimal decomposition without phase
space discretization. Moreover, several simulation examples are given to
illustrate the effectiveness of the proposed method
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
A Framework for Globally Optimizing Mixed-Integer Signomial Programs
Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers. © 2013 Springer Science+Business Media New York
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