numerical analysis of a transient non linear axisymmetric eddy current model this paper deals with the numerical solution of an axisymmetric transient eddy current problem in a conductive non linear magnetic media this means that the relation between the magnetic field and the magnetic induction i e the so called b h curve is non linear we analyze a weak formulation of the resulting problem in the axisymmetric case with the source term given by means of a non homogeneous dirichlet boundary condition for its numerical approximation we propose a fully discrete scheme based on a finite element method combined with a backward euler time discretization we establish its well posedness and derive error estimates in appropriate norms for the proposed scheme in particular we obtain an l 2 rate of convergence of order o h t without assuming any additional regularity of the solution moreover under appropriate smoothness assumptions we also prove an l 2 like rate of convergence of order o h 2 t finally some numerical results which confirm the theoretically predicted behavior of the method are reported

bounding the bias of contrastive divergence learning optimization based on k step contrastive divergence cd has become a common way to train restricted boltzmann machines rbms the k step cd is a biased estimator of the log likelihood gradient relying on gibbs sampling we derive a new upper bound for this bias its magnitude depends on k the number of variables in the rbm and the maximum change in energy that can be produced by changing a single variable the last reflects the dependence on the absolute values of the rbm parameters the magnitude of the bias is also affected by the distance in variation between the modeled distribution and the starting distribution of the gibbs chain

efficient algorithm for nonconvex minimization and its application to pm regularization in image processing nonconvex regularization has the ability to smooth homogeneous regions and sharpen edges but leads to challenging computation we propose some iterative schemes to minimize the energy function with nonconvex edge preserving potential the schemes are derived from the duality based algorithm proposed by bermudez and moreno and the fixed point iteration the convergence is proved for the convex energy function with nonconvex potential and the linear convergence rate is given applying the proposed schemes to perona and malik s nonconvex regularization we present some efficient algorithms based on our schemes and show the approximate convergence behavior for nonconvex energy function experimental results are presented which show the efficiency of our algorithms including better denoised performance of nonconvex regularization faster convergence speed higher calculation precision lower calculation cost under the same number of iterations and less implementation time under the same peak signal noise ratio level

a duality method for the compressible reynolds equation application to simulation of read write processes in magnetic storage devices in this work the authors present a new numerical algorithm to approximate the solution of compressible reynolds equation with additional first order slip flow terms this equation appears when modelling read write processes in magnetic storage devices such as hard disks the proposed numerical method is based on characteristics approximation for convection dominating terms and a duality method applied to a maximal monotone operator which represents the nonlinear diffusive term several test examples illustrate the good performance of the method

numerical discretization of a darcy forchheimer model we solve a steady darcy forchheimer flow in a bounded region by means of piecewise constant velocities and nonconforming piecewise mathbb p 1 pressures for the computation we solve the nonlinearity by an alternating directions algorithm and we decouple the computation of the velocity from that of the pressure by a gradient algorithm we prove a priori error estimates of the scheme and convergence of the alternating directions algorithm

a penalty finite element approximation to a signorini two body contact problem in thermoelasticity in this work a numerical approximation by the finite element method of a quasi static frictionless unilateral contact problem between two thermoelastic bodies in two dimensions is considered the approximation scheme is based on a penalty formulation used to replace the signorini contact condition convergence results and error bounds are obtained and some numerical experiments presented

analysis of two frictional viscoplastic contact problems with damage in this work we study two quasistatic frictional contact problems arising in viscoplasticity including the mechanical damage of the material caused by excessive stress or strain and modelled by an inclusion of parabolic type the variational formulation is provided for both problems and the existence of a unique solution is proved for each of them then a fully discrete scheme is introduced using the finite element method to approximate the spatial domain and the euler scheme to discretize the time derivatives error estimates are derived and under suitable regularity assumptions the linear convergence of the algorithm is deduced finally some numerical examples are presented to show the performance of the method

numerical methods for a fixed domain formulation of the glacier profile problem with alternative boundary conditions in this paper we develop a set of numerical techniques for the simulation of the profile evolution of a valley glacier in the framework of isothermal shallow ice approximation models the different mathematical formulations are given in terms of a highly nonlinear parabolic equation a first nonlinearity comes from the free boundary problem associated with the unknown basal extension of the glacier region this feature is treated using a fixed domain complementarity formulation which is solved numerically by a duality method the nonlinear diffusive term is explicitly treated in the time marching scheme a convection dominated problem arises so a characteristic scheme is proposed for the time discretization while piecewise linear finite elements are used for the spatial discretization the presence of infinite slopes in polar regimes motivates an alternative formulation based on a prescribed flux boundary condition at the head of the glacier instead a homogeneous dirichlet one finally several numerical examples illustrate the performance of the proposed methods

mathematical analysis and numerical solution of models with dynamic preisach hysteresis abstract hysteresis is a phenomenon that is observed in a great variety of physical systems which leads to a nonlinear and multivalued behavior making their modeling and control difficult even though the analysis and mathematical properties of several rate independent and rate dependent hysteresis models are known this is not the case for the bertotti s rate dependent extension of the classical preisach model the so called dynamic preisach model for which current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics both being crucial in practice this paper deals with the description and mathematical analysis of the dynamic preisach hysteresis model toward that end we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field h and the magnetic induction b in which the values of b not only depends on the present values of h but also on the past history and its velocity we first analyze mathematically some important properties of the model and compare them with known results for the static preisach model then we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations under suitable assumptions we prove the existence of a solution of a weak formulation of the problem and solve it numerically finally we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic preisach model

numerical analysis of a frictional contact problem for viscoelastic materials with long term memory we consider a mathematical model which describes the bilateral contact between a deformable body and an obstacle the process is quasistatic the material is assumed to be viscoelastic with long memory and the friction is modeled with tresca s law the problem has a unique weak solution here we study spatially semi discrete and fully discrete schemes using finite differences and finite elements we show the convergence of the schemes under the basic solution regularity and we derive order error estimates finally we present an algorithm for the numerical realization and simulations for a two dimensional test problem

learning harmonium models with infinite latent features undirected latent variable models represent an important class of graphical models that have been successfully developed to deal with various tasks one common challenge in learning such models is to determine the number of hidden units that are unknown a priori although bayesian nonparametrics have provided promising results in bypassing the model selection problem in learning directed bayesian networks very little effort has been made toward applying bayesian nonparametrics to learn undirected latent variable models in this paper we present the infinite exponential family harmonium iefh a bipartite undirected latent variable model that automatically determines the number of latent units from an unbounded pool we also present two important extensions of iefh to 1 multiview iefh for dealing with heterogeneous data and 2 infinite maximum margin harmonium immh for incorporating supervising side information to learn predictive latent features we develop variational inference algorithms to learn model parameters our methods are computationally competitive because of the avoidance of selecting the number of latent units our extensive experiments on real image datasets and text datasets appear to demonstrate the benefits of iefh and immh inherited from bayesian nonparametrics and max margin learning such results were not available until now and contribute to expanding the scope of bayesian nonparametrics to learn the structures of undirected latent variable models

on the convergence of the bermudez moreno algorithm with constant parameters bermudez moreno 5 presents a duality numerical algorithm for solving variational inequalities of the second kind the performance of this algorithm strongly depends on the choice of two constant parameters assuming a further hypothesis of the inf sup type we present here a convergence theorem that improves on the one presented in 5 we prove that the convergence is linear and we give the expression of the asymptotic error constant and the explicit form of the optimal parameters as a function of some constants related to the variational inequality finally we present some numerical examples that confirm the theoretical results

numerical approach of temperature distribution in a free boundary model for polythermal ice sheets a numerical method for solving the thermal subproblem appearing in the modelization of polythermal ice sheets is described this thermal problem mainly involves three nonlinearities a reaction term due to the viscous dissipation a signorini boundary condition associated to the geothermic flux and an enthalpy term issued from the two phase stefan formulation of the polythermal regime the stationary temperature is obtained as the limit of an evolutive problem which is discretized in time with an upwind characteristics scheme and in space with finite elements the nonlinearities are solved either by newton raphson method or by duality techniques applied to maximal monotone operators the application of the algorithms provides the dimensionless temperature distribution approximation and allows to identify the cold and temperate ice regions

bouncing towards the optimum improving the results of monte carlo optimization algorithms simulated annealing and related monte carlo type optimization algorithms are used to apply statistical physics concepts in particular ideas from the statistical mechanics of spin glasses to find optimal configurations for combinatorial optimization problems there are formal proofs showing that these algorithms converge asymptotically i e possibly for infinitely long simulation times to a global optimum practical implementations however only allow for finite simulation times and thus the annealing process is often trapped in energetically higher suboptimal configurations in this work we present an algorithm we call it bouncing which takes the final low energy configuration of e g a conventional monotonically cooled annealing run as an input and subjects it to a schedule of repeatedly reheating and cooling the maximum of a susceptibility and a specific heat like quantity sampled during the initial monotonic cooling process serve as lower and upper starting temperature bounds for this secondary heating and cooling we present in addition to a serial implementation a recipe for a parallel computer and provide a number of results showing the success of the bouncing method for a particularly prominent example of a combinatorial optimization problem the traveling salesman problem

justifying and generalizing contrastive divergence we study an expansion of the log likelihood in undirected graphical models such as the restricted boltzmann machine rbm where each term in the expansion is associated with a sample in a gibbs chain alternating between two random variables the visible vector and the hidden vector in rbms we are particularly interested in estimators of the gradient of the log likelihood obtained through this expansion we show that its residual term converges to zero justifying the use of a truncation running only a short gibbs chain which is the main idea behind the contrastive divergence cd estimator of the log likelihood gradient by truncating even more we obtain a stochastic reconstruction error related through a mean field approximation to the reconstruction error often used to train autoassociators and stacked autoassociators the derivation is not specific to the particular parametric forms used in rbms and requires only convergence of the gibbs chain we present theoretical and empirical evidence linking the number of gibbs steps k and the magnitude of the rbm parameters to the bias in the cd estimator these experiments also suggest that the sign of the cd estimator is correct most of the time even when the bias is large so that cd k is a good descent direction even for small k

an elastic viscoplastic quasistatic contact problem with damage abstract in this paper the contact between an elastic viscoplastic body and a deformable obstacle is studied the effect of the damage due to tension or compression is also considered the variational formulation leads to a coupled system of evolutionary equations for which an existence and uniqueness result is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are obtained and as a consequence the convergence of the algorithm is deduced finally some numerical simulations are presented to demonstrate the accuracy of the algorithm

numerical analysis and simulations of a quasistatic frictional contact problem with damage in viscoelasticity we consider a quasistatic problem which models the bilateral contact between a viscoelastic body and a foundation taking into account the damage and the friction the damage which results from tension or compression is then involved in the constitutive law and it is modelled using a nonlinear parabolic inclusion the variational problem is formulated as a coupled system of evolutionary equations for which we state the existence of a unique solution then we introduce a fully discrete scheme using the finite element method to approximate the spatial variable and the euler scheme to discretize the time derivatives error estimates are derived and under suitable regularity hypotheses the convergence of the numerical scheme obtained finally a numerical algorithm and results are presented for some two dimensional examples

nonlinear optimization simplified by hypersurface deformation a general strategy is advanced for simplifying nonlinear optimization problems the ant lion method this approach exploits shape modifications of the costfunction hypersurface which distend basins surrounding low lying minima including global minima by intertwining hypersurface deformations with steepest descent displacements the search is concentrated on a small relevant subset of all minima specific calculations demonstrating the value of this method are reported for the partitioning of two classes of irregular but nonrandom graphs the prime factor graphs and the pi graphs we also indicate how this approach can be applied to the traveling salesman problem and to design layout optimization and that it may be useful in combination with simulated annealing strategies

numerical upscaling of the free boundary dam problem in multiscale high contrast media abstract in this paper we address the numerical homogenization approximation of a free boundary dam problem posed in a heterogeneous media more precisely we propose a generalized multiscale finite element method gmsfem for the heterogeneous dam problem the motivation of using the gmsfem approach comes from the multiscale nature of the porous media due to its high contrast permeability thus although we can classically formulate the free boundary dam problem as in the homogeneous case a very high resolution will be needed by a standard finite element approximation in order to obtain realistic results that recover the multiscale nature first we introduce a fictitious time variable which motivates a suitable time discretization that can be understood as a fixed point iteration to the steady state solution and we use a duality method to deal with the involved multivalued nonlinear terms next we compute efficient approximations of the pressure and the saturation by using the gmsfem method and we can identify the free boundary more precisely the gmsfem method provides numerical results that capture the behavior of the solution due to the variations of the coefficient at the fine resolution by just solving linear systems with the size proportional to the number of coarse blocks of a coarse grid that does not need to be adapted to the variations of the coefficient finally we present illustrative numerical results to validate the proposed methodology

numerical analysis of a frictionless contact problem for elastic viscoplastic materials abstract we consider a mathematical model which describes the unilateral quasistatic contact of two elastic viscoplastic bodies the contact is without friction and it is modeled by the classical signorini boundary conditions the model consists of an evolution equation coupled with a time dependent variational inequality it has been shown that the variational problem of the model has a unique solution here we consider numerical approximations of the problem we use the finite element method to discretize the spatial domain spatially semi discrete and fully discrete schemes are studied for both schemes we show the existence of a unique solution and derive error estimates under appropriate regularity assumptions of the solution we have the optimal order convergence

on the neighborhood structure of the traveling salesman problem generated by local search moves when trying to find approximate solutions for the traveling salesman problem with heuristic optimization algorithms small moves called lin k opts are often used in our paper we provide exact formulas for the numbers of possible tours into which a randomly chosen tour can be changed with a lin k opt furthermore we compare the quality of the results to which the various moves lead

packing a multidisperse system of hard disks in a circular environment we consider the problem of finding the densest closed packing of hard disks with proposed different radii in a circular environment such that the radius of the circumcircle is minimal with our approach we are able to find denser packings for various problem instances than known from the literature both for the dynamics of the simulation and for the optimum values of the radii of the circumcircles we find various scaling laws

the numerical solution of some elliptic nonscalar problems with nonlinear discontinuities abstract this paper is devoted to the numerical solution of some semilinear elliptic systems with nonlinear discontinuities the motivation is the modelling of single irreversible nonisothermic stationary reactions of zero order the numerical solution is achieved through an iterative procedure this uses exact regularization we justify the convergence of the algorithm and also we present some numerical results

how to center deep boltzmann machines this work analyzes centered restricted boltzmann machines rbms and centered deep boltzmann machines dbms where centering is done by subtracting offset values from visible and hidden variables we show analytically that i centered and normal boltzmann machines bms and thus rbms and dbms are different parameterizations of the same model class such that any normal bm rbm dbm can be transformed to an equivalent centered bm rbm dbm and vice versa and that this equivalence generalizes to artificial neural networks in general ii the expected performance of centered binary bms rbms dbms is invariant under simultaneous flip of data and offsets for any off set value in the range of zero to one iii centering can be reformulated as a different update rule for normal bms rbms dbms and iv using the enhanced gradient is equivalent to setting the offset values to the average over model and data mean furthermore we present numerical simulations suggesting that i optimal generative performance is achieved by subtracting mean values from visible as well as hidden variables ii centered binary rbms dbms reach significantly higher log likelihood values than normal binary rbms dbms iii centering variants whose offsets depend on the model mean like the enhanced gradient suffer from severe divergence problems iv learning is stabilized if an exponentially moving average over the batch means is used for the offset values instead of the current batch mean which also prevents the enhanced gradient from severe divergence v on a similar level of log likelihood values centered binary rbms dbms have smaller weights and bigger bias parameters than normal binary rbms dbms vi centering leads to an update direction that is closer to the natural gradient which is extremely efficient for training as we show for small binary rbms vii centering eliminates the need for greedy layer wise pre training of dbms which often even deteriorates the results independently of whether centering is used or not and ix centering is also beneficial for auto encoders

interior penalty methods for finite element approximations of the signorini problem in elastostatics abstract the use of interior penalty methods as a basis for developing finite element approximations of boundary value problems with constraints is explored particular attention is given to the signorini problem of contact of an elastic body with a rigid foundation error estimates are derived and the results of a numerical experiment are discussed

efficient numerical schemes for viscoplastic avalanches part 1 the 1d case this paper deals with the numerical resolution of a shallow water viscoplastic flow model viscoplastic materials are characterized by the existence of a yield stress below a certain critical threshold in the imposed stress there is no deformation and the material behaves like a rigid solid but when that yield value is exceeded the material flows like a fluid in the context of avalanches it means that after going down a slope the material can stop and its free surface has a non trivial shape as opposed to the case of water newtonian fluid the model involves variational inequalities associated with the yield threshold finite volume schemes are used together with duality methods namely augmented lagrangian and bermudez moreno to discretize the problem to be able to accurately simulate the stopping behavior of the avalanche new schemes need to be designed involving the classical notion of well balancing in the present context it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet dry fronts which are encountered in geophysical geometries we derived such schemes and numerical experiments are presented to show their performances

piecewise linear approximation of the continuous rudin osher fatemi model for image denoising this paper is concerned with the numerical approximation of the minimizer of the continuous rudin osher fatemi rof model for image denoising a new discrete total variation is proposed and the associated hilbertian total variation denoising model is used to construct continuous piecewise linear functions that approximate the minimizer of the rof model in the strong topology of l 2 omega provided that the data function is bounded and weakly regular in the sense of text lip alpha text l 2 omega

on a doubly nonlinear parabolic obstacle problem modelling ice sheet dynamics this paper deals with the weak formulation of a free moving boundary problem arising in theoretical glaciology considering shallow ice sheet flow we present the mathematical analysis and the numerical solution of the second order nonlinear degenerate parabolic equation modelling in the isothermal case the ice sheet non newtonian dynamics an obstacle problem is then deduced and analyzed the existence of a free boundary generated by the support of the solution is proved and its location and evolution are qualitatively described by using a comparison principle and an energy method then the solutions are numerically computed with a method of characteristics and a duality algorithm to deal with the resulting variational inequalities the weak framework we introduce and its analysis both qualitative and numerical are not restricted to the simple physics of the ice sheet model we consider nor to the model dimension they can be successfully applied to more realistic and sophisticated models related to other geophysical settings

attractor dynamics in feedforward neural networks we study the probabilistic generative models parameterized by feedforward neural networks an attractor dynamics for probabilistic inference in these models is derived from a mean field approximation for large layered sigmoidal networks fixed points of the dynamics correspond to solutions of the mean field equations which relate the statistics of each unit to those of its markov blanket we establish global convergence of the dynamics by providing a lyapunov function and show that the dynamics generate the signals required for unsupervised learning our results for feedforward networks provide a counterpart to those of cohen grossberg and hopfield for symmetric networks

numerical solution of cavitation problems in lubrication abstract a combination of the method of characteristics and of the finite element method is applied to solve numerically a stationary free boundary problem of hydrodynamic lubrication with cavitation the discretization leads to a system of nonlinear equations to solve it a duality iterative algorithm is used numerical results are presented

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a computational study of smoothing heuristics for the traveling salesman problem abstract over the last five years or so data smoothing has been used to improve the performance of heuristics that solve combinatorial optimization problems data smoothing allows a local search heuristic to escape from a poor local optimum in practice data smoothing has worked well when applied to the traveling salesman problem in this paper we conduct an extensive computational study to test the performance of eight smoothing heuristics for the traveling salesman problem in particular we apply eight smoothing heuristics and standard versions of two opt and three opt to 40 randomly generated euclidean problems and 30 problems taken from a well known library of test problems we compare the solutions generated by the heuristics and provide insight into the behavior of the smoothing heuristics

duality methods for solving variational inequalities abstract methods of maximal monotone operators are used in order to study from a general point of view duality numerical algorithms for solving variational inequalities with classical algorithms such as uzawa s method for the standard and augmented lagrangian this paper presents some new algorithms which appear to have very good numerical performances

a fast learning algorithm for deep belief nets we show how to use complementary priors to eliminate the explaining away effects that make inference difficult in densely connected belief nets that have many hidden layers using complementary priors we derive a fast greedy algorithm that can learn deep directed belief networks one layer at a time provided the top two layers form an undirected associative memory the fast greedy algorithm is used to initialize a slower learning procedure that fine tunes the weights using a contrastive version of the wake sleep algorithm after fine tuning a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels this generative model gives better digit classification than the best discriminative learning algorithms the low dimensional manifolds on which the digits lie are modeled by long ravines in the free energy landscape of the top level associative memory and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind

record breaking optimization results using the ruin and recreate principle a new optimization principle is presented solutions of problems are partly but significantly ruined and rebuilt or recreated afterwards performing this type of change frequently one can obtain astounding results for classical optimization problems the new method is particularly suited for more complex optimization problems discontinuous ones problems with hard to find admissible solutions problems with complex objectives or many constraints the method is an all purpose heuristic numerical results are given for the traveling salesman problem for the vehicle routing problem with time windows and for network optimization numerical evidence for the quality of the proposed principle is given for most of the instances of a research library of problems the ruin and recreate r r implementation achieved the best published results for many instances better or much better solutions could be found

threshold accepting a general purpose optimization algorithm appearing superior to simulated annealing abstract a new general purpose algorithm for the solution of combinatorial optimization problems is presented the new threshold accepting method is even simpler structured than the wellknown simulated annealing approach the power of the new algorithm is demonstrated by computational results concerning the traveling salesman problem and the problem of the construction of error correcting codes moreover deterministic versions of the new heuristic turn out to perform nearly equally well consuming only a fraction of the computing time of the stochastic versions as an example the deterministic threshold accepting method yields very near to optimum tours for the famous 442 cities traveling salesman problem of grotschel within 1 to 2 s of cpu time

search space smoothing for combinatorial optimization problems commonly there are two types of local search approaches known to treat combinatorial optimization problems with very complex search space structure one is to introduce very complicated types of local move classes allowing a bypass of high energetic barriers separating different minima the second is introducing a control parameter i e temperature in physics terminology dependent state space walker which is depending on this control parameter more or less easily able to climb over barriers a third less well known but very obvious approach is to smooth the search space i e to eliminate barriers between low energy configurations and therefore to allow a fast and easy approach to the global optimum this procedure will be discussed in depth in the following work

critical point approximation through exact regularization construction d algorithmes iteratifs pour la resolution des problemes extremaux non differentiables regularisation d une fonctionnelle application aux problemes differentiels semi elliptiques en physique des plasmas et en mecanique des fluides

duality methods with an automatic choice of parameters application to shallow water equations in conservative form in 3 a duality numerical algorithm for solving variational inequalities based on certain properties of the yosida approximation of maximal monotone operators has been introduced the performance of this algorithm strongly depends on the choice of two constant parameters in this paper we consider a new class of algorithms where these constant parameters are replaced by functions we show that convergence properties are preserved and look for optimal values of these two functions in general these optimal values cannot be computed as they depend on the exact solution therefore we propose some strategies in order to approximate them the resulting algorithms are applied to three variational inequalities in order to compare their performance with that of the original algorithm

a novel parameter estimation method for boltzmann machines we propose a novel estimator for a specific class of probabilistic models on discrete spaces such as the boltzmann machine the proposed estimator is derived from minimization of a convex risk function and can be constructed without calculating the normalization constant whose computational cost is exponential order we investigate statistical properties of the proposed estimator such as consistency and asymptotic normality in the framework of the estimating function small experiments show that the proposed estimator can attain comparable performance to the maximum likelihood expectation at a much lower computational cost and is applicable to high dimensional data

a membrane in adhesive contact a model for the process of quasi static evolution of an elastic membrane in adhesive contact with a rigid obstacle is developed analyzed and numerically simulated the model consists of an elliptic variational inequality for the membrane displacements and a nonlinear ordinary differential equation for the evolution of the adhesion field by using regularity results from the theory of elliptic variational inequalities and a fixed point argument the system is shown to have a unique weak solution a fully discrete algorithm is described and shown to converge and its error estimates are derived in this process we make critical use of the regularity properties of the solution finally the results of numerical simulations based on the fully discrete algorithm are presented

characteristics method for the formulation and computation of a free boundary cavitation problem in this paper a semidiscretized scheme based on characteristics method is analyzed when it is applied to a free boundary problem the free boundary problem issued from a cavitation model in lubrication involves specific boundary conditions the idea is to associate to the departure problem a sequence of variational inequalities depending on a discretization parameter the theoretical convergence result from the solution of the semidiscretized problem to the solution of the continuous one is stated for a flux imposed boundary condition for this purpose due to the specific boundary conditions technical modifications of the classical version of characteristics are needed then obstacle problem tools are applied to a set of variational inequalities with neumann boundary conditions in order to obtain l estimates which provide the convergence result in this way a result of existence of solution for the continuous problem and a theoretical justification for the usage of the proposed numerical methods are concluded finally some numerical test examples are presented to illustrate the good performance of the method

box relaxation schemes in staggered discretizations for the dual formulation of total variation minimization in this paper we propose some new box relaxation numerical schemes on staggered grids to solve the stationary system of partial differential equations arising from the dual minimization problem associated with the total variation operator we present in detail the numerical schemes for the scalar case and its generalization to multichannel vectorial images then we discuss their implementation in digital image denoising the results outperform the resolution of the dual equation based on the gradient descent approach and pave the way for more advanced numerical strategies

finite elements numerical solution of a coupled profile velocity temperature shallow ice sheet approximation model this work deals with the numerical solution of a complex mathematical model arising in theoretical glaciology the global moving boundary problem governs thermomechanical processes jointly with ice sheet hydrodynamics one major novelty is the inclusion of the ice velocity field computation in the framework of the shallow ice model so that it can be coupled with profile and temperature equations moreover the proposed basal velocity and shear stress laws allow the integration of basal sliding effects in the global model both features were not taking into account in a previous paper math model methods appl sci 12 2 2002 229 and provide more realistic convective terms and more complete signorini boundary conditions for the thermal problem in the proposed numerical algorithm one and two dimensional piecewise linear lagrange finite elements in space and a semi implicit upwinding scheme in time are combined with duality and newton s methods for nonlinearities a simulation example involving real data issued from antarctic shows the temperature profile and velocity qualitative behaviour as well as the free boundaries and basal effects

reinforcement learning with factored states and actions a novel approximation method is presented for approximating the value function and selecting good actions for markov decision processes with large state and action spaces the method approximates state action values as negative free energies in an undirected graphical model called a product of experts the model parameters can be learned efficiently because values and derivatives can be efficiently computed for a product of experts actions can be found even in large factored action spaces by the use of markov chain monte carlo sampling simulation results show that the product of experts approximation can be used to solve large problems in one simulation it is used to find actions in action spaces of size 240

algorithms for estimating the partition function of restricted boltzmann machines abstract accurate estimates of the normalization constants partition functions of energy based probabilistic models markov random fields are highly important for example for assessing the performance of models monitoring training progress and conducting likelihood ratio tests several algorithms for estimating the partition function in relation to a reference distribution have been introduced including annealed importance sampling ais and bennett s acceptance ratio method bar however their conceptual similarities and differences have not been worked out so far and systematic comparisons of their behavior in practice have been missing we devise a unifying theoretical framework for these algorithms which comprises existing variants and suggests new approaches it is based on a generalized form of crooks equality linking the expectation over a distribution of samples generated by a transition operator to the expectation over the distribution induced by the reversed operator the framework covers different ways of generating samples such as parallel tempering and path sampling an empirical comparison revealed the differences between the methods when estimating the partition function of restricted boltzmann machines and ising models in our experiments bar using parallel tempering worked well with a small number of bridging distributions while path sampling based ais performed best when many bridging distributions were available because bar gave the overall best results we favor it over ais furthermore the experiments showed the importance of choosing a proper reference distribution

a generalized duality method for solving variational inequalities applications to some nonlinear dirichlet problems in 2 bermudez and moreno introduced a duality algorithm for the numerical solution of variational inequalities this algorithm is based on some properties of the yosida regularization of maximal monotone operators the performances of this algorithm strongly depend on the choice of two constant parameters a generalization of the algorithm with automatic choice of parameters was discussed in 13 where the constant parameters were replaced by scalar functions thus improving the convergence of the algorithm in this article we present a generalization of the bermudez moreno algorithm that allows the use of very general operators as parameters extending some of the results in 2 13 and 14 as a particular case we analyze the use of scalar and matrix valued parameters in a lp m context we apply the results developed to some boundary value problems involving the p laplacian operator where it is shown that the use of matrix valued parameters improves the convergence of the algorithm

numerical approximation of the elastic viscoplastic contact problem with non matching meshes this work deals with the approximation of a time dependent variational inequality modelling the unilateral contact problem of elastic viscoplastic bodies in a bidimensional context the problem is approximated in the space variable with nonconforming finite element methods which allow the handling of nonmatching meshes on the contact zone several error estimates are established and the corresponding numerical experiments are achieved

new optimization heuristics in a former paper we introduced a very effective new general purpose optimization principle we compared this method which we called threshold accepting ta with the well known simulated annealing sa method for discrete optimization the empirical results demonstrated the superiority of the ta algorithm in further experiments with the ta principle we discovered two new powerful optimization heuristics the great deluge algorithm gda and the record to record travel rrt these algorithms resemble in their structure the formerly studied ta and the sa method the differences lie in their acceptance rules for worse intermediate solutions both the gda and the rrt are essentially one parameter algorithms i e for the achievement of best possible performance a good choice is necessary only for a single parameter this is in contrast for instance to the classical as algorithm where it is necessary to choose carefully a certain sequence of parameters the so called annealing schedule the quality of the computational results obtained so far by rrt and gda shows that the new algorithms behave equally well as ta and thus a fortiori better than sa

a numerical algorithm for a signorini problem associated with maxwell norton materials by using generalized newton s methods abstract the goal of this work is to present new numerical approaches to obtain computationally efficient adaptive procedures to solve contact problems associated with maxwell norton materials we will describe in detail the numerical methods used to solve such problems and derive iterative algorithms to validate the proposed algorithms we will present some test examples with known analytical solutions finally we will compare the efficiency of the algorithms presented in this paper with others previously proposed by the authors

traveling salesman problem and tsallis statistics a generalization of the stochastic method of simulated annealing algorithm based on tsallis statistics is proposed this algorithm is considerably faster than the traditional ones in solving the traveling salesman problem acceptable solutions are found in fewer steps and higher temperatures than both the classical and the fast simulated annealings recent developments in solving np complete problems can be incorporated and improve the performance even more

bias variance decompositions for likelihood based estimators the bias variance decomposition of mean squared error is well understood and relatively straightforward in this note a similar simple decomposition is derived valid for any kind of error measure that when using the appropriate probability model can be derived from a kullback leibler divergence or log likelihood

numerical solving of frictionless contact problems in perfectly plastic bodies abstract we consider the frictionless unilateral contact problems of a perfectly plastic solid with a rigid foundation and two perfectly plastic solids under an analogous variational formulation for each one we introduce a discrete approximation via the finite element method and in due course prove convergence also we introduce a converging iterative algorithm to the solution of the discrete problems and present some numerical experiences

training products of experts by minimizing contrastive divergence it is possible to combine multiple latent variable models of the same data by multiplying their probability distributions together and then renormalizing this way of combining individual expert models makes it hard to generate samples from the combined model but easy to infer the values of the latent variables of each expert because the combination rule ensures that the latent variables of different experts are conditionally independent when given the data a product of experts poe is therefore an interesting candidate for a perceptual system in which rapid inference is vital and generation is unnecessary training a poe by maximizing the likelihood of the data is difficult because it is hard even to approximate the derivatives of the renormalization term in the combination rule fortunately a poe can be trained using a different objective function called contrastive divergence whose derivatives with regard to the parameters can be approximated accurately and efficiently examples are presented of contrastive divergence learning using several types of expert on several types of data

traveling salesman problem with clustering in the original traveling salesman problem the traveling salesman has the task to find the shortest closed tour through a proposed set of nodes touching each node exactly once and returning to the initial node at the end for the sake of the tour length to be minimized nodes close to each other might not be visited one after the other but separated in the tour however for some practical applications it is useful to group nodes to clusters such that all nodes of a cluster are visited contiguously here we present an approach which leads to an automatic clustering with a clustering parameter governing the sizes of the clusters

simulated tempering procedure for spin glass simulations we develop an appropriate iteration procedure for the determination of the parameters for the method of simulated tempering and test it successfully on the two dimensional ising spin glass the reduction of the slowing down is comparable to that of the multicanonical algorithm simulated tempering has however the advantages of allowing full vectorization of the programs and of providing the canonical ensemble directly

variable neighbourhood structures for cycle location problems abstract variable neighbourhood search is a metaheuristic used mainly to tackle combinatorial optimization problems its performance depends on having a good variable neighbourhood structure that is a sequence of neighbourhoods that are ideally pairwise disjoint and contain feasible solutions further and further from a given feasible solution this article defines a variable neighbourhood structure with these properties that is new for cycle location problems it find bounds for the neighbourhood sizes and shows how to iterate over then when the cycle is a circuit it tests the structure and iteration method using variable neighbourhood search on a range of median cycle problems and finds a neighbourhood size beyond which there is on average no benefit in applying local search this neighbourhood size is found not to depend on problem size or bound on circuit length

finite element methods for constrained problems in elasticity several different variational formulations of boundary value problems with constraints are discussed with particular reference to constrained problems in elasticity special attention is given to exterior penalty methods a discussion of the conditions necessary for penalty methods to provide a basis for stable and convergent finite element methods is given in particular the use of reduced integration is discussed and criteria on the order of reduced integration rules sufficient to produce stable and convergent schemes are described applications of reduced integration penalty methods to incompressible elasticity problems and contact problems are described

finite element approximation of nonlinear transient magnetic problems involving periodic potential drop excitations abstract this paper deals with the computation of nonlinear 2d transient magnetic fields when the data concerning the electric current sources involve potential drop excitations in the first part a mathematical model is stated which is solved by an implicit time discretization scheme combined with a finite element method for space approximation the second part focuses on developing a numerical method to compute periodic solutions by determining a suitable initial current which avoids large simulations to reach the steady state this numerical method leads to solve a nonlinear system of equations which requires to approximate several nonlinear and linear magnetostatic problems the proposed methods are first validated with an axisymmetric example and sinusoidal source having an analytical solution then we show the saving in computational effort that this methodology offers to approximate practical problems specially with pulse width modulation pwm voltage supply

a convergence result in the study of bone remodeling contact problems we consider the approximation of a bone remodeling model with the signorini contact conditions by a contact problem with normal compliant obstacle when the obstacle s deformability coefficient converges to zero that is the obstacle s stiffness tends to infinity the variational problem is a coupled system composed of a nonlinear variational equation in the case of normal compliance contact conditions or a variational inequality for the case of signorini s contact conditions for the mechanical displacement field and a first order ordinary differential equation for the bone remodeling function a theoretical result which states the convergence of the contact problem with normal compliance contact law to the signorini problem is then proved finally some numerical simulations involving examples in one and two dimensions are reported to show this convergence behaviour

flow regulation for water quality restoration in a river section modeling and control this work is devoted to the numerical resolution of an optimal control problem that arises in the management of a reservoir for the remediation of a polluted river section by using mathematical modeling and optimal control techniques we set the mathematical formulation of the problem as a hyperbolic optimal control problem with control constraints and obtain a fully discretized problem finally we propose a gradient free method to solve it and present realistic numerical results

numerical analysis of a viscoplastic problem with contact condition taking place in an aluminium casting we consider a viscoplastic problem with contact condition modelling the thermomechanical deformations during casting of aluminium alloy slabs we introduce a fictitious domain method to impose the metallostatic pressure on the thermal free boundary finally we present some numerical results for a particular casting process during both the start and stationary stages

numerical analysis of a frictionless viscoelastic contact problem with normal damped response abstract we consider a mathematical model which describes the frictionless contact between a viscoelastic body and a deformable foundation we model the material s behavior with a nonlinear kelvin voigt constitutive law the process is assumed to be quasistatic and the contact is modeled with a general normal damped response condition we present the variational formulation of the problem including the existence of a unique weak solution to the model we then study the numerical approach to the problem using a fully discrete finite elements scheme with an explicit discretization in time we state the existence of the unique solution for the scheme and derive an error estimate on the approximate solutions finally we present some numerical results involving examples in one and two dimensions

on the augmented lagrangian approach to signorini elastic contact problem the signorini problem describes the contact of a linearly elastic body with a rigid frictionless foundation it is transformed into a saddle point problem of some augmented lagrangian functional and then discretized by finite element methods optimal error estimates are obtained for general smooth domains which are not necessarily convex the key ingredient in the analysis is a discrete inf sup condition which guarantees the existence of the saddle point

a bound for the convergence rate of parallel tempering for sampling restricted boltzmann machines sampling from restricted boltzmann machines rbms is done by markov chain monte carlo mcmc methods the faster the convergence of the markov chain the more efficiently can high quality samples be obtained this is also important for robust training of rbms which usually relies on sampling parallel tempering pt an mcmc method that maintains several replicas of the original chain at higher temperatures has been successfully applied for rbm training we present the first analysis of the convergence rate of pt for sampling from binary rbms the resulting bound on the rate of convergence of the pt markov chain shows an exponential dependency on the size of one layer and the absolute values of the rbm parameters it is minimized by a uniform spacing of the inverse temperatures which is often used in practice similarly as in the derivation of bounds on the approximation error for contrastive divergence learning our bound on the mixing time implies an upper bound on the error of the gradient approximation when the method is used for rbm training

damageable contact between an elastic body and a rigid foundation in this work the contact problem between an elastic body and a rigid obstacle is studied including the development of material damage which results from internal compression or tension the variational problem is formulated as a first kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field the existence of a unique local weak solution is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are derived on the approximate solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions finally three two dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme

influence of rounding errors on the quality of heuristic optimization algorithms abstract search space smoothing and related heuristic optimization algorithms provide an alternative approach to simulated annealing and its variants while simulated annealing traverses barriers in the energy landscape at finite temperatures search space smoothing intends to remove these barriers so that a greedy algorithm is sufficient to find the global minimum several formulas for smoothing the energy landscape have already been applied one of them making use of the finite numerical precision on a computer in this paper we thoroughly investigate the effect of finite numerical accuracy on the quality of results achieved with heuristic optimization algorithms we present computational results for the traveling salesman problem

numerical analysis and simulations of a dynamic frictionless contact problem with damage the process of dynamic frictionless contact between a viscoelastic body and a reactive foundation which includes material damage is modelled numerically analyzed and simulated contact is modelled with the normal compliance condition the damage of the material resulting from tension or compression is described by the damage field which measures the pointwise fractional decrease in the load carrying capacity of the material the evolution of the damage is governed by a parabolic differential inclusion a fully discrete scheme for the problem is proposed and error estimates on the numerical solutions derived the scheme has been implemented and numerical simulations of the evolution of the mechanical state of the system and its material damage are presented