an efficient two phase rm l 1 tv method for restoring blurred images with impulse noise a two phase image restoration method based upon total variation regularization combined with an l1 data fitting term for impulse noise removal and deblurring is proposed in the first phase suitable noise detectors are used for identifying image pixels contaminated by noise then in the second phase based upon the information on the location of noise free pixels images are deblurred and denoised simultaneously for efficiency reasons in the second phase a superlinearly convergent algorithm based upon fenchel duality and inexact semismooth newton techniques is utilized for solving the associated variational problem numerical results prove the new method to be a significantly advance over several state of the art techniques with respect to restoration capability and computational efficiency

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

the primal dual active set strategy as a semismooth newton method this paper addresses complementarity problems motivated by constrained optimal control problems it is shown that the primal dual active set strategy which is known to be extremely efficient for this class of problems and a specific semismooth newton method lead to identical algorithms the notion of slant differentiability is recalled and it is argued that the max function is slantly differentiable in lp spaces when appropriately combined with a two norm concept this leads to new local convergence results of the primal dual active set strategy global unconditional convergence results are obtained by means of appropriate merit functions

on generalized painleve chains abstract painleve chains are recursively defined sequences of dominant truncations of polynomial partial differential equations in this paper a new kind of painleve chain is defined which can lead to new branches of the painleve expansions associated to the dominant truncations applying methods of hlavaty a recursion relation for the resonances of the members of these chains is deduced a special case is considered in detail

a multi scale vectorial l τ tv framework for color image restoration a general multi scale vectorial total variation model with spatially adapted regularization parameter for color image restoration is introduced in this paper this total variation model contains an l data fidelity for any c 1 2 the use of a spatial dependent regularization parameter improves the reconstruction of features in the image as well as an adequate smoothing for the homogeneous parts the automated adaptation of this regularization parameter is made according to local statistical characteristics of the noise which contaminates the image the corresponding multiscale vectorial total variation model is solved by fenchel duality and inexact semismooth newton techniques numerical results are presented for the cases 1 and 2 which reconstruct images contaminated with salt and pepper noise and gaussian noise respectively

regularity results for the quasi static bingham variational inequality in dimensions two and three we consider the variational inequality describing the stationary flow of a bingham type fluid in bounded domains differentiability properties of weak solutions in suitable energy spaces providing existence theorems are studied we suppose that the volume forces belong to classes of morrey type and generalize our previous regularity results concerning slow steady state flow of bingham fluids

convergence of an iterative method for total variation denoising in total variation denoising one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion several approaches based on this idea have recently been shown to be very effective particularly for denoising functions with discontinuities this paper analyzes the convergence of an iterative method for solving such problems the iterative method involves a lagged diffusivity approach in which a sequence of linear diffusion problems are solved global convergence in a finite dimensional setting is established and local convergence properties including rates and their dependence on various parameters are examined

global and superlinear convergence of the smoothing newton method and its application to general box constrained variational inequalities the smoothing newton method for solving a system of nonsmooth equations f x 0 which may arise from the nonlinear complementarity problem the variational inequality problem or other problems can be regarded as a variant of the smoothing method at the kth step the nonsmooth function f is approximated by a smooth function f and the derivative of f at x k is used as the newton iterative matrix the merits of smoothing methods and smoothing newton methods are global convergence and convenience in handling in this paper we show that the smoothing newton method is also superlinearly convergent if f is semismooth at the solution and f satisfies a jacobian consistency property we show that most common smooth functions such as the gabriel more function have this property as an application we show that for box constrained variational inequalities if the involved function is p uniform the iteration sequence generated by the smoothing newton method will converge to the unique solution of the problem globally and superlinearly quadratically

homotopy method for solving variational inequalities with bounded box constraints abstract in this paper using the gabriel more smoothing function of the median function a smooth homotopy method for solving nonsmooth equation reformulation of bounded box constrained variational inequality problem vip l u f is given without any monotonicity condition on the defining map f for starting point chosen almost everywhere in r n existence and convergence of the homotopy pathway are proven nevertheless it is also proven that if the starting point is chosen to be an interior point of the box the proposed homotopy method can also serve as an interior point method

a posteriori error estimation for a pde constrained optimization problem involving the generalized oseen equations we derive globally reliable a posteriori error estimators for a linear quadratic optimal control problem involving the generalized oseen equations as state equations control constraints are also considered the corresponding local error indicators are locally efficient the assumptions under which we perform the analysis are such that they can be satisfied for a wide variety of stabilized finite element methods as well as for standard finite element methods when stabilized methods are considered no a priori relation between the stabilization terms for the state and adjoint equations is required if a lower bound for the inf sup constant is available a posteriori error estimators that are fully computable and provide guaranteed upper bounds on the norm of the error can be obtained we illustrate the theory with numerical examples

numerical simulation of two dimensional bingham fluid flow by semismooth newton methods this paper is devoted to the numerical simulation of two dimensional stationary bingham fluid flow by semismooth newton methods we analyze the modeling variational inequality of the second kind considering both dirichlet and stress free boundary conditions a family of tikhonov regularized problems is proposed and the convergence of the regularized solutions to the original one is verified by using fenchel s duality optimality systems which characterize the original and regularized solutions are obtained the regularized optimality systems are discretized using a finite element method with cross grid p 1 q 0 elements for the velocity and pressure respectively a semismooth newton algorithm is proposed in order to solve the discretized optimality systems using an additional relaxation a descent direction is constructed from each semismooth newton iteration local superlinear convergence of the method is also proved finally we perform numerical experiments in order to investigate the behavior and efficiency of the method

strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems it is well known that the eigenvalues of a real symmetric matrix are not everywhere differentiable a classical result of ky fan states that each eigenvalue of a symmetric matrix is the difference of two convex functions which implies that the eigenvalues are semismooth functions based on a recent result of the authors it is further proved in this paper that the eigenvalues of a symmetric matrix are strongly semismooth everywhere as an application it is demonstrated how this result can be used to analyze the quadratic convergence of newton s method for solving inverse eigenvalue problems ieps and generalized ieps with multiple eigenvalues

semi smooth newton methods for state constrained optimal control problems abstract a regularized optimality system for state constrained optimal control problems is introduced and semi smooth newton methods for its solution are analyzed convergence of the regularized problems is proved numerical tests confirm the theoretical results and demonstrate the efficiency of the proposed methodology

on the painleve classification of partial differential equations semilinear second order partial differential equations in two independent variables with rational right hand side are investigated it is found that the painleve admissible pdes can be transformed to a form with maximally three poles a complete list of pdes that pass the test for the painleve property is given

a multilevel algorithm for simultaneously denoising and deblurring images in this paper we develop a fast multilevel algorithm for simultaneously denoising and deblurring images under the total variation regularization although much effort has been devoted to developing fast algorithms for the numerical solution and the denoising problem was satisfactorily solved fast algorithms for the combined denoising and deblurring model remain to be a challenge recently several successful studies of approximating this model and subsequently finding fast algorithms were conducted which have partially solved this problem the aim of this paper is to generalize a fast multilevel denoising method to solving the minimization model for simultaneously denoising and deblurring our new idea is to overcome the complexity issue by a detailed study of the structured matrices that are associated with the blurring operator a fast algorithm can then be obtained for directly solving the variational model supporting numerical experiments on gray scale images are presented

projection and self adaptive projection methods for the signorini problem with the bem abstract we propose two new projection methods for solving the signorini problem and study the relationship between them since the signorini boundary condition is equivalent to a projection fixed point problem the methods formulate the signorini boundary condition into a sequence of robin boundary conditions and only require solving a variational problem with simple boundary conditions at each iterative step the convergence speed of the first method depends on the parameter heavily and it is difficult to choose a proper for individual problems to improve the efficiency of the method we propose an adaptive projection method which adjusts the parameter automatically per iteration we establish the convergence analysis of the methods because the signorini boundary condition is given in an iterative form by the potential and its derivative on the boundary of the domain we can easily provide the boundary element approximation of the problem finally we present some numerical simulations which illustrate the performance of the methods

an augmented lagrangian method for optimization problems in banach spaces we propose a variant of the classical augmented lagrangian method for constrained optimization problems in banach spaces our theoretical framework does not require any convexity or second order assumptions and it allows the treatment of inequality constraints with infinite dimensional image space moreover we discuss the convergence properties of our algorithm with regard to feasibility global optimality and kkt conditions some numerical results are given to illustrate the practical viability of the method

total bounded variation regularization as a bilaterally constrained optimization problem it is demonstrated that the predual for problems with total bounded variation regularization terms can be expressed as a bilaterally constrained optimization problem existence of a lagrange multiplier and an optimality system are established this allows us to utilize efficient optimization methods developed for problems with box constraints in the context of bounded variation formulations here in particular the primal dual active set method considered as a semismooth newton method is analyzed and superlinear convergence is proved as a by product we obtain that the lagrange multiplier associated with the box constraints acts as an edge detector numerical results for image denoising and zooming resizing show the efficiency of the new approach

an adaptive finite element method for bingham fluid flows around a cylinder the numerical modeling of the steady flow of a yield stress fluid around a cylinder is presented three categories of yielded regions are exhibited the asymptotic behavior when the cylinder gets close to the wall is investigated the resolution of variational inequalities describing the flow is based on the augmented lagrangian method and a mixed finite element method the localization of yield surfaces is approximated by an anisotropic auto adaptive mesh procedure

on large deviations theory and asymptotically efficient monte carlo estimation it is shown how large deviations theory can be applied to construct an asymptotically efficient simulation distribution for monte carlo simulation using the importance sampling technique a sufficient and necessary condition is given for the asymptotic efficiency of the candidate simulation distributions this is done in the multidimensional setting that is required by many practical simulation problems the result obtained is applied primarily in two areas first the generalization of previous work dealing with functionals of markov chains is discussed a second area of application is the simulation of nonlinear systems with gaussian inputs as an example of a system with gaussian inputs the simulation of a digital communication channel with nonlinear isi intersymbol interference characteristic of satellite data links is considered in the case of linear isi the asymptotically efficient exponentially twisted distribution turns out to agree with a method previously proposed by d lu and k yao 1988 the large deviations point of view provides some useful insight on how to extent the lu and yao method to nonlinear channels

the painleve classification dominant truncations and resonance analysis a classification of ode from the point of view of singular point analysis is suggested the general formula for the painleve resonances is derived and the resonance analysis of low order dominant truncations is performed the resonance formulae for the painleve chains are presented and the significance of the painleve chains for the classification is explained

some quadrature based versions of the generalized newton method for solving nonsmooth equations abstract in this paper modifications of a generalized newton method based on some rules of quadrature are studied the methods considered are newton like iterative schemes for numerical solving systems of nonsmooth equations some mild conditions are given that ensure superlinear convergence to a solution moreover a parameterized version of the midpoint version is presented finally results of numerical tests are established

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

regularized state constrained boundary optimal control of the navier stokes equations abstract the numerical solution of the dirichlet boundary optimal control problem of the navier stokes equations in presence of pointwise state constraints is investigated two different regularization techniques are considered first a moreau yosida regularization of the problem is studied optimality conditions are derived and the convergence of the regularized solutions towards the original one is proved a source representation of the control combined with a lavrentiev type regularization strategy is also presented the analysis concerning optimality conditions and convergence of the regularized solutions is carried out in the last part of the paper numerical experiments are presented for the numerical solution of each regularized problem a semi smooth newton method is applied

two projection methods for the solution of signorini problems abstract two iterative methods based on projection and boundary element methods are considered for signorini problems the regularized problem with the projection boundary condition is first deduced from the signorini problem by using the equivalence between the signorini boundary condition and the projection fixed point problem our methods formulate the signorini boundary condition into a sequence of robin boundary conditions in the new boundary condition there is a penalty parameter the convergence speed of the first method is greatly influenced by the value of which is difficult to choose for individual problems to improve the performance of this method we present a self adaptive projection method which adjusts the parameter automatically per iteration based on the iterative data the main result of this work is to provide the convergence of the methods under mild assumptions as the iteration process is given by the potential and its derivative on the boundary of the domain the unknowns of the problem are computed explicitly by using the boundary element method both theoretical results and numerical experiments indicate efficiency of the methods proposed

a total variation based approach to correcting surface coil magnetic resonance images abstract magnetic resonance images which are corrupted by noise and by smooth modulations are corrected using a variational formulation incorporating a total variation like penalty for the image and a high order penalty for the modulation the optimality system is derived and numerically discretized the cost functional used is non convex but it possesses a bilinear structure which allows the ambiguity among solutions to be resolved technically by regularization and practically by normalizing the maximum value of the modulation since the cost is convex in each single argument convex analysis is used to formulate the optimality condition for the image in terms of a primal dual system to solve the optimality system a nonlinear gauss seidel outer iteration is used in which the cost is minimized with respect to one variable after the other using an inner generalized newton iteration favorable computational results are shown for artificial phantoms as well as for realistic magnetic resonance images reported computational times demonstrate the feasibility of the approach in practice

nonlinear evolution equations of hamiltonian form and the painleve analysis a number of necessary conditions for a class of nonlinear partial differential equations to pass the painleve test with the kruskal ansatz is given a theory for the admissible resonance patterns of equations in hamiltonian form is developed and discussed for some important special cases based on these results on algorithm can be described which constructs all nonlinear evolution equations of normal type and a certain hamiltonian form

on the density of classes of closed convex sets with pointwise constraints in sobolev spaces abstract for a banach space x of r m valued functions on a lipschitz domain let k x x be a closed convex set arising from pointwise constraints on the value of the function its gradient or its divergence respectively the main result of the paper establishes under certain conditions the density of k x 0 in k x 1 where x 0 is densely and continuously embedded in x 1 the proof is constructive utilizes the theory of mollifiers and can be applied to sobolev spaces such as h 0 div and w 0 1 p in particular it is also shown that such a density result cannot be expected in general

universal simulation distributions in this paper we present a new class of importance sampling simulation distributions the universal distributions we show that these distributions are universally efficient in the sense that they depend only on a single scalar parameter regardless of the dimensionality of the underlying system or of the error sets to be simulated

on the asymptotic efficiency of importance sampling techniques the asymptotic efficiency of importance sampling is techniques for the simulation of rare events in a multidimensional nonlinear setting was studied by j s sadowsky and j a bucklew see ibid vol 36 p 579 88 1990 fundamental results on the asymptotic efficiency of the mean value modification mm technique were derived additionally a statement was made that other is techniques cannot be asymptotically efficient it is shown that for the simulation of digital communication systems with gaussian input a broad class of asymptotically efficient is techniques exists necessary and sufficient conditions are provided for the asymptotic efficiency of five different is techniques including mm for one dimensional linear systems multidimensional generalizations of these is techniques are proposed a sufficient condition for the asymptotic efficiency of these techniques applied to multidimensional nonlinear systems is provided

overlapping domain decomposition methods for total variation denoising alternating and parallel overlapping domain decomposition methods for the minimization of the total variation are presented their derivation is based on the predual formulation of the total variat

importance sampling simulation for evaluating lower bound symbol error rate of the bayesian dfe with multilevel signaling schemes for the class of equalizers that employs a symbol decision finite memory structure with decision feedback the optimal solution is known to be the bayesian decision feedback equalizer dfe the complexity of the bayesian dfe however increases exponentially with the length of the channel impulse response cir and the size of the symbol constellation conventional monte carlo simulation for evaluating the symbol error rate ser of the bayesian dfe becomes impossible for high channel signal to noise ratio snr conditions it has been noted that the optimal bayesian decision boundary separating any two neighboring signal classes is asymptotically piecewise linear and consists of several hyperplanes when the snr tends to infinity this asymptotic property can be exploited for efficient simulation of the bayesian dfe an importance sampling is simulation technique is presented based on this asymptotic property for evaluating the lower bound ser of the bayesian dfe with a multilevel pulse amplitude modulation m pam scheme under the assumption of correct decisions being fed back a design procedure is developed which chooses appropriate bias vectors for the simulation density to ensure asymptotic efficiency ae of the is simulation

path following methods for a class of constrained minimization problems in function space path following methods for primal dual active set strategies requiring a regularization parameter are introduced existence of a primal dual path and its differentiability properties are analyzed monotonicity and convexity of the primal dual path value function are investigated both feasible and infeasible approximations are considered numerical path following strategies are developed and their efficiency is demonstrated by means of examples

combined symmetric bem and semi smooth newton method for the contact problems in linear elasticity of yukawa type the semi smooth newton method and the boundary element method are developed and analyzed for the solution of 2 d signorini contact problems in linear elasticity of yukawa type first we consider the contact problem with tresca friction this leads to a constrained non differentiable minimization problem where the solvability is in general problematic but by utilizing the fenchel duality theory the dual formulation in terms of contact stresses turns out to be a quadratic optimization problem with a smooth functional the regularization of the dual problem motivated by the augmented lagrangian is suitable for the application of the generalized newton method applying the boundary integral equation method the problem is reduced to the boundary curve the corresponding boundary integral equations are approximated by using a galerkin method with the help of b splines on the boundary curve bem this yields an algebraic system of linear equations with dense stiffness matrix but which is symmetric the symmetry property of the stiffness matrix enables the application of efficient iterative solution strategies for the linear systems at each newton step second the methods are carried over to the coulomb friction problem by means of a fixed point approach in particular the analysis of the algorithm is presented and some numerical examples which show a remarkable efficiency and reliability of the semi smooth newton method are given

superlinear convergence of smoothing quasi newton methods for nonsmooth equations abstract we study local convergence of smoothing quasi newton methods for solving a system of nonsmooth nondifferentiable equations in r n the feature of smoothing quasi newton methods is to use a smooth function to approximate the nonsmooth mapping and update the quasi newton matrix at each step convergence results are given under directional derivative consistence property without differentiability we establish a dennis more type superlinear convergence theorem for smoothing quasi newton methods and we prove linear convergence of the smoothing broyden method furthermore we propose a superlinear convergent smoothing newton broyden method without using the generalized jacobian and the semismooth assumption we illustrate the smoothing approach on box constrained variational inequalities

path following and augmented lagrangian methods for contact problems in linear elasticity a certain regularization technique for contact problems leads to a family of problems that can be solved efficiently using infinite dimensional semismooth newton methods or in this case equivalently primal dual active set strategies we present two procedures that use a sequence of regularized problems to obtain the solution of the original contact problem first order augmented lagrangian and path following methods the first strategy is based on a multiplier update while path following with respect to the regularization parameter uses theoretical results about the path value function to increase the regularization parameter appropriately comprehensive numerical tests investigate the performance of the proposed strategies for both a 2d as well as a 3d contact problem

newton and quasi newton methods for a class of nonsmooth equations and related problems the paper presents concrete realizations of quasi newton methods for solving several standard problems including complementarity problems special variational inequality problems and the karush kuhn tucker kkt system of nonlinear programming a new approximation idea is introduced in this paper the q superlinear convergence of the newton method and the quasi newton method are established under suitable assumptions in which the existence of f x is not assumed the new algorithms only need to solve a linear equation in each step for complementarity problems the qr factorization on the quasi newton method is discussed

augmented lagrangian method applied to american option pricing the american option pricing problem is originally formulated as a stochastic optimal stopping time problem it is also equivalent to a variational inequality problem or a complementarity problem involving the black scholes partial differential operator in this paper the corresponding variational inequality problem is discretized by using a fitted finite volume method based on the discretized form an algorithm is developed by applying augmented lagrangian method alm to the valuation of the american option convergence properties of alm are considered by empirical numerical experiments we conclude that alm is more effective than penalty method and lagrangian method and comparable with the projected successive overrelaxation method psor furthermore numerical results show that alm is more robust in terms of computation time under changes in market parameters interest rate and volatility

primal dual active set strategy for a general class of constrained optimal control problems an algorithm for efficient solution of optimal control problems with pointwise constraints is introduced it is based on an active set strategy using primal as well as dual variables under certain assumptions a decrease of an appropriately chosen merit function and convergence of the algorithm are proved numerical examples for a parabolic optimal control problem demonstrate the efficiency of the proposed method for control constrained problems

the structure of optimal parameters for image restoration problems in cambridge this project has been supported by king abdullah university of science and technology kaust award no kuk i1 007 43 epsrc grants nr ep j009539 1 sparse higher order image restoration and nr ep m00483x 1 efficient computational tools for inverse imaging problems in quito the project has been supported by the escuela politecnica nacional de quito under award pis 12 14 and the mathamsud project socde sparse optimal control of differential equations when in quito t valkonen was moreover supported by a prometeo scholarship of the senescyt ecuadorian ministry of science technology education and innovation

convergence analysis of some algorithms for solving nonsmooth equations this paper presents convergence analysis of some algorithms for solving systems of nonlinear equations defined by locally lipschitzian functions for the directional derivative based and the generalized jacobian based newton methods both the iterates and the corresponding function values are locally superlinearly convergent globally a limiting point of the iterate sequence generated by the damped directional derivative based newton method is a zero of the system if and only if the iterate sequence converges to this point and the stepsize eventually becomes one provided that the system is strongly bd regular and semismooth at this point in this case the convergence is superlinear a general attraction theorem is presented which can be applied to two algorithms proposed by han pang and rangaraj a hybrid method which is both globally convergent in the sense of finding a stationary point of the norm function of the system and locally quadratically convergent is also presented

application of a first order operator splitting method to bingham fluid flow simulation abstract we discuss here a first order operator splitting method for the solution of the time dependent variational inequality modeling the flow of a bingham visco plastic medium at each time step we shall have to solve a nonlinear elliptic problem then a nondifferentiable minimization problem and finally a stokes type problem the first problem is solved by a fixed point method the second one happens to be a saddle point problem for a lagrangian functional and we shall use an uzawa algorithm to solve it the last problem is solved by a conjugate gradient method we have applied this splitting method to two test problems the first one has a forcing term with homogeneous dirichlet boundary conditions while the second one concerns the simulation of the flow of a bingham fluid in a wall driven cavity our results compare very well with the ones obtained by solving directly the variational inequality mentioned above

can the nonlocal characterization of sobolev spaces by bourgain et al be useful for solving variational problems we question whether the recent characterization of sobolev spaces by bourgain brezis and mironescu 2001 could be useful to solve variational problems on w 1 p omega to answer this we introduce a sequence of functionals so that the seminorm is approximated by an integral operator involving a differential quotient and a radial mollifier then for the approximated formulation we prove existence uniqueness and convergence of the solution to the unique solution of the initial formulation we show that these results can also be extended in the bv case interestingly this approximation leads to a unified implementation for sobolev spaces including with high p values and for the bv space finally we show how this theoretical study can indeed lead to a numerically tractable implementation and we give some image diffusion results as an illustration

an adaptive fixed point proximity algorithm for solving total variation denoising models abstract we study an adaptive fixed point proximity algorithm to solve the total variation denoising model the objective function is a sum of two convex functions and one of them is composed by an affine transformation which is usually a regularization term by decoupling and splitting the problem is changed into two subproblems due to the nonsmooth and nondifferentiability of the subproblem we solve its proximity minimization problem instead of the original one to overcome the staircase effect during the process of denoising an adaptive criterion on proximity parameters is put forward at last we apply the improved algorithm to solve the isotropic total variation denoising model the numerical results are given to illustrate the efficiency of the algorithm

a system of nonsmooth equations solver based upon subgradient method in this paper a subgradient method is developed to solve the system of nonsmooth equations first the system of nonsmooth equations is transformed into a nonsmooth optimization problem with zero minimal objective function value then a subgradient method is applied to solve the nonsmooth optimization problem during the processes the pre known optimal objective function value is adopted to update step sizes the corresponding convergence results are established as well several numerical experiments and applications show that the proposed method is efficient and robust

secant methods for semismooth equations some generalizations of the secant method to semismooth equations are presented in the one dimensional case the superlinear convergence of the classical secant method for general semismooth equations is proved moreover a new quadratically convergent method is proposed that requires two function values per iteration for the n dimensional cases we discuss secant methods for two classes of composite semismooth equations most often studied semismooth equations are of such form

an infeasible primal dual algorithm for total bounded variation based inf convolution type image restoration in this paper a primal dual algorithm for total bounded variation tv type image restoration is analyzed and tested analytically it turns out that employing a global boldsymbol l s regularization with 1 s leq 2 in the dual problem results in a local smoothing of the tv regularization term in the primal problem the local smoothing can alternatively be obtained as the infimal convolution of the ell r norm with r 1 s 1 1 and a smooth function in the case r s 2 this results in gauss tv type image restoration the globalized primal dual algorithm introduced in this paper works with generalized derivatives converges locally at a superlinear rate and is stable with respect to noise in the data in addition it utilizes a projection technique which reduces the size of the linear system that has to be solved per iteration a comprehensive numerical study ends the paper

model based control of dynamic frictional contact problems using the example of hot rolling abstract we consider hot forming processes in which a metal solid body is deformed by several rolls in order to obtain a desired final shape to minimize cutting scrap and to ensure that this shape satisfies the required tolerances as precisely as possible we formulate an optimal control problem where we use the trajectories of the rolls as control functions the deformation of the solid body is described through the basic equations of nonlinear continuum mechanics which are here coupled with an elasto viscoplastic material model based on a multiplicative split of the deformation gradient we assume that the deformations of the rolls can be neglected thus we add unilateral frictional contact boundary conditions resulting in an evolutionary quasi variational inclusion the associated control to observation map is non differentiable due to changes of state between elastic and plastic material behavior contact and separation and stick and slip motion yet we still want to apply gradient based methods to solve the optimal control problem and therefore have to make sure that derivatives of cost functional and constraints exist to resolve this issue we first regularize all non differentiabilities and subsequently apply the direct differentiation method to obtain sensitivity information finally we formulate a suitable algorithm and discuss numerical results for a real world example to illustrate its capability

a two step model for image denoising using a duality strategy and surface fitting in order to alleviate the staircase effect or the edge blurring in the course of the image denoising we propose a two step model based on the duality strategy in fact this strategy follows the observation that the dual variable of the restored image can be looked at as the normal vector so we first obtain the dual variable and then reconstruct the image by fitting the dual variable following the augmented lagrangian strategy we propose a projection gradient method for solving this two step model we also give some convergence analyses of the proposed projection gradient method several numerical experiments are tested to compare our proposed model with the rof model and the llt model

an investigation of gaussian tail and rayleigh tail density functions for importance sampling digital communication system simulation the gains achieved by the use of importance sampling in communication system simulation are strongly influenced by the choice of the biased input noise distribution the rayleigh tail and the gaussian tail distributions are investigated for use as biased distributions in importance sampling the robustness of these schemes with respect to the estimate of the unknown error probability is examined it is shown that the gaussian tail distribution previously considered to be theoretically optimum is not optimum in this regard methods of generating the biased random variates are presented

a primal dual active set strategy for optimal boundary control of a nonlinear reaction diffusion system this paper is concerned with optimal boundary control of an instationary reaction diffusion system in three spatial dimensions this problem involves a coupled nonlinear system of parabolic differential equations with bilateral as well as integral control constraints we include the integral constraint in the cost by a penalty term whereas the bilateral control constraints are handled explicitly first and second order conditions for the optimization problem are analyzed a primal dual active set strategy is utilized to compute optimal solutions numerically the algorithm is compared to a semismooth newton method

an admm numerical approach to linear parabolic state constrained optimal control problems optimal control problems arising from systems modeled by linear parabolic equations may be difficult for both theoretical analysis and algorithmic design for the case where there are additional constraints on the state variables restrictive regularity assumptions are usually required to guarantee the existence of the associated lagrange multiplier and thus some regularization type methods such as the moreau yosida and lavrentiev methods have been discussed in the literature in this article we study the application of the alternating direction method of multipliers admm to linear parabolic state constrained optimal control problems and propose an admm numerical approach we prove the convergence of the admm algorithm without any existence or regularity assumption on the lagrange multiplier and estimate its worst case convergence rate in both the ergodic and nonergodic senses an important feature of the admm approach is that it decouples the state constraints and the parabolic optimal control problems inside each iteration we show the efficiency of the admm approach by testing some control problems in two space dimensions

a family of second order methods for convex ell _1 l1 regularized optimization this paper is concerned with the minimization of an objective that is the sum of a convex function f and an ell 1 l1 regularization term our interest is in active set methods that incorporate second order information about the function f to accelerate convergence we describe a semismooth newton framework that can be used to generate a variety of second order methods including block active set methods orthant based methods and a second order iterative soft thresholding method the paper proposes a new active set method that performs multiple changes in the active manifold estimate at every iteration and employs a mechanism for correcting these estimates when needed this corrective mechanism is also evaluated in an orthant based method numerical tests comparing the performance of three active set methods are presented

an iterative method for the stokes type problem with variable viscosity this paper concerns an iterative technique for solving discretized stokes type equations with varying viscosity coefficient we build a special block preconditioner for the discrete system of equations and perform an analysis revealing its properties the theoretical analysis is based on the weighted necas inequality the subject of this paper is motivated by numerical solution of incompressible non newtonian fluid equations in particular the general analysis is applied to the linearized equations of the regularized bingham model of viscoplastic fluid numerical experiments show that the suggested preconditioner leads to an iterative method insensitive to the variation of mesh size and the regularization parameter of the fluid model

a quasisecant method for solving a system of nonsmooth equations in this paper the solution of nonsmooth equations is studied we first transform the problem into an equivalent nonsmooth optimization problem and then the quasisecant method is introduced to solve it some nonsmooth equations that have arisen from bilevel programming problems are solved by our proposed method the numerical results show the effectiveness and efficiency of our proposed method

painleve chains for the study of integrable higher order differential equations the concept of painleve chains is extended to chains of ordinary differential equations obtained by successive and simultaneous differentiation of both sides of equations of the general type f chi u ux u2x unx g chi u ux u2x umx where m or n 1 the three painleve chains are thus generated by such successive differentiation of u2x ku2 kdv chain u2x ku3 modified kdv chain and ux ku2 burgers chain hybrid painleve chains can be analogously obtained by successive differentiation of hybrid differential equations such chains obtained from u2x uux u3 and u2x 3uux u3 are described in detail passive differential equations in which the balancing exponent must depend upon the coefficients can also lead analogously to painleve chains as illustrated by those obtained from u2x ku2x u where k 2 or 3 2 the schwarzian derivative u3x ux 3 2 u2x ux 2 generates a painleve chain in which the members have consecutive integral resonances starting with the ubiquitous 1 chains of higher order differential equations exhibiting some but not all of the features of painleve chains can be obtained from the second order eigenvalue problem the dominant truncations of most evolution equations as well as the painleve canonical equations including the irreducible painleve transcendents appear in painleve chains generated these methods

an absolutely stable pressure poisson stabilized finite element method for the stokes equations the pressure poisson stabilized galerkin method for the stokes equation requires the choice of a positive parameter existing theoretical predictions for the range of parameter values that yield stable discretizations seem to be very pessimistic when compared to the computational evidence motivated by this wide gap we first examine a continuous prototype for this class of schemes we show that the prototype is absolutely stable i e it is stable for all parameter values and is optimally accurate we then define a new practical variant of the well known pressure poisson stabilized scheme we prove that the new method is absolutely stable just like its continuous prototype and that it achieves optimal convergence rates with respect to the same mesh independent norms the new method differs from the standard pressure poisson stabilized method in several important aspects first its definition does not degrade to a penalty formulation for the lowest order nodal spaces second the method is absolutely stable with respect to the natural norm for the problem while the standard pressure poisson stabilized method is stable with respect to a mesh dependent norm

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

high order total variation based image restoration the total variation tv denoising method is a pde based technique that preserves edges well but has the sometimes undesirable staircase effect namely the transformation of smooth regions ramps into piecewise constant regions stairs in this paper we present an improved model constructed by adding a nonlinear fourth order diffusive term to the euler lagrange equations of the variational tv model our technique substantially reduces the staircase effect while preserving sharp jump discontinuities edges we show numerical evidence of the power of resolution of this novel model with respect to the tv model in some 1d and 2d numerical examples

a primal dual active set method for non negativity constrained total variation deblurring problems this paper studies image deblurring problems using a total variation based model with a non negativity constraint the addition of the non negativity constraint improves the quality of the solutions but makes the solution process a difficult one the contribution of our work is a fast and robust numerical algorithm to solve the non negatively constrained problem to overcome the nondifferentiability of the total variation norm we formulate the constrained deblurring problem as a primal dual program which is a variant of the formulation proposed by chan golub and mulet for unconstrained problems here dual refers to a combination of the lagrangian and fenchel duals to solve the constrained primal dual program we use a semi smooth newton s method we exploit the relationship between the semi smooth newton s method and the primal dual active set method to achieve considerable simplification of the computations the main advantages of our proposed scheme are no parameters need significant adjustment a standard inverse preconditioner works very well quadratic rate of local convergence theoretical and numerical numerical evidence of global convergence and high accuracy of solving the optimality system the scheme shows robustness of performance over a wide range of parameters a comprehensive set of numerical comparisons are provided against other methods to solve the same problem which show the speed and accuracy advantages of our scheme

new control allocation algorithms in fixed point framework for overactuated systems with actuator saturation abstractin this paper two control allocation algorithms have been proposed for overactuated systems the algorithms are developed by formulating constrained control allocation problem into an equivalent fixed point framework the first algorithm follows sequential solving method while the other one involves a zero finding technique by the newton method in order to consider limiting constraints the saturation function has been taken into account that leads to a nonsmooth zero finding problem and the proposed method guarantees superlinear convergence the second algorithm is easy to implement and faster than the algorithm developed based on the sequential solving technique to demonstrate the effectiveness of the proposed algorithms a detail simulation study has been carried out in which one example considers both the actuator rate and amplitude constraints

systematics of strongly self dominant higher order differential equations based on the painleve analysis of their singularities this paper presents a simple way of classifying higher order differential equations based on the requirements of the painleve property i e the presence of no movable critical points the fundamental building blocks for such equations may be generated by strongly self dominant differential equations of the type x nu xm u m n p p in which m and n are positive integers and p is a negative integer such differential equations having both a constant degree d and a constant value of the difference n m form a painleve chain however only three of the many possible painleve chains can have the painleve property among the three painleve chains that can have the painleve property one contains the burgers equation another contains the dominant terms of the first painleve transcendent the isospectral korteweg de vries equation and the isospectral boussinesq equation and the third contains the dominant terms of the second painleve transcendent and the isospectral modified cubic korteweg de vr

the primal dual active set method for nonlinear optimal control problems with bilateral constraints the primal dual active set method has proved to be an efficient numerical tool in the context of diverse applications so far it has been investigated mainly for linear problems this paper is devoted to the study of global convergence of the primal dual active set method for nonlinear problems with bilateral constraints utilizing the close relationship between the primal dual active set method and semismooth newton methods local superlinear convergence of the method is investigated as well

semismooth newton and augmented lagrangian methods for a simplified friction problem in this paper a simplified friction problem and iterative second order algorithms for its solution are analyzed in infinite dimensional function spaces motivated from the dual formulation a primal dual active set strategy and a semismooth newton method for a regularized problem as well as an augmented lagrangian method for the original problem are presented and their close relation is analyzed local as well as global convergence results are given by means of numerical tests we discuss among others convergence properties the dependence on the mesh and the role of the regularization and illustrate the efficiency of the proposed methodologies