1,793 research outputs found
MAP inference via Block-Coordinate Frank-Wolfe Algorithm
We present a new proximal bundle method for Maximum-A-Posteriori (MAP)
inference in structured energy minimization problems. The method optimizes a
Lagrangean relaxation of the original energy minimization problem using a multi
plane block-coordinate Frank-Wolfe method that takes advantage of the specific
structure of the Lagrangean decomposition. We show empirically that our method
outperforms state-of-the-art Lagrangean decomposition based algorithms on some
challenging Markov Random Field, multi-label discrete tomography and graph
matching problems
A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching
We study the quadratic assignment problem, in computer vision also known as
graph matching. Two leading solvers for this problem optimize the Lagrange
decomposition duals with sub-gradient and dual ascent (also known as message
passing) updates. We explore s direction further and propose several additional
Lagrangean relaxations of the graph matching problem along with corresponding
algorithms, which are all based on a common dual ascent framework. Our
extensive empirical evaluation gives several theoretical insights and suggests
a new state-of-the-art any-time solver for the considered problem. Our
improvement over state-of-the-art is particularly visible on a new dataset with
large-scale sparse problem instances containing more than 500 graph nodes each.Comment: Added acknowledgment
Low energy dynamics of U(1)^{N} Chern-Simons solitons
We apply the adiabatic approximation to investigate the low energy dynamics
of vortices in the parity invariant double self-dual Higgs model with only
mutual Chern-Simons interaction. When distances between solitons are large they
are particles subject to the mutual interaction. The dual formulation of the
model is derived to explain the sign of the statistical interaction. When
vortices of different types pass one through another they behave like charged
particles in magnetic field. They can form a bound state due to the mutual
magnetic trapping. Vortices of the same type exhibit no statistical
interaction. Their short range interactions are analysed. Possible quantum
effects due to the finite width of vortices are discussed.Comment: keywords: vortex, vortices, anyons, fractional statistics, 20 pages
in Latex, accepted for publication in Phys.Rev.D, ( the above keywords
missing in the title were added
Lagrangean decomposition for large-scale two-stage stochastic mixed 0-1 problems
In this paper we study solution methods for solving the dual problem corresponding to the Lagrangean Decomposition of two stage stochastic mixed 0-1 models. We represent the two stage stochastic mixed 0-1 problem by a splitting variable representation of the deterministic equivalent model, where 0-1 and continuous variables appear at any stage. Lagrangean Decomposition is proposed for satisfying both the integrality constraints for the 0-1 variables and the non-anticipativity constraints. We compare the performance of four iterative algorithms based on dual Lagrangean Decomposition schemes, as the Subgradient method, the Volume algorithm, the Progressive Hedging algorithm and the Dynamic Constrained Cutting Plane scheme. We test the conditions and properties of convergence for medium and large-scale dimension stochastic problems. Computational results are reported.Progressive Hedging algorithm, volume algorithm, Lagrangean decomposition, subgradient method
Theory and computation of higher gradient elasticity theories based on action principles
In continuum mechanics, there exists a unique theory for elasticity, which includes the first gradient of displacement. The corresponding generalization of elasticity is referred to as strain gradient elasticity or higher gradient theories, where the second and higher gradients of displacement are involved. Unfortunately, there is a lack of consensus among scientists how to achieve the generalization. Various suggestions were made, in order to compare or even verify these, we need a generic computational tool. In this paper, we follow an unusual but quite convenient way of formulation based on action principles. First, in order to present its benefits, we start with the action principle leading to the well-known form of elasticity theory and present a variational formulation in order to obtain a weak form. Second, we generalize elasticity and point out, in which term the suggested formalism differs. By using the same approach, we obtain a weak form for strain gradient elasticity. The weak forms for elasticity and for strain gradient elasticity are solved numerically by using open-source packages—by using the finite element method in space and finite difference method in time. We present some applications from elasticity as well as strain gradient elasticity and simulate the so-called size effect
Reformulation and decomposition of integer programs
In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe column generation and the resulting branch-and-price algorithms. This is followed by an examination of Benders’ type algorithms based on projection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.Integer program, Lagrangean relaxation, column generation, branch-and-price, extended formulation, Benders' algorithm
Stress relaxation models with polyconvex entropy in Lagrangean and Eulerian coordinates
The embedding of the equations of polyconvex elastodynamics to an augmented
symmetric hyperbolic system provides in conjunction with the relative entropy method
a robust stability framework for approximate solutions \cite{LT06}.
We devise here a model of stress relaxation motivated by the
format of the enlargement process which formally approximates
the equations of polyconvex elastodynamics. The model is endowed with
an entropy function which is not convex but rather of polyconvex type.
Using the relative entropy we prove a stability estimate and convergence
of the stress relaxation model to polyconvex elastodynamics in the
smooth regime. As an application, we show that models of pressure relaxation for
real gases in Eulerian coordinates fit into the proposed framework
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