exact penalty results for mathematical programs with vanishing constraints a mathematical program with vanishing constraints mpvc is a constrained optimization problem arising in certain engineering applications the feasible set has a complicated structure so that the most familiar constraint qualifications are usually violated this in turn implies that standard penalty functions are typically non exact for mpvcs we therefore develop a new mpvc tailored penalty function which is shown to be exact under reasonable assumptions this new penalty function can then be used to derive or recover suitable optimality conditions for mpvcs

strongly stable c stationary points for mathematical programs with complementarity constraints in this paper we consider the class of mathematical programs with complementarity constraints mpcc under an appropriate constraint qualification of mangasarian fromovitz type we present a topological and an equivalent algebraic characterization of a strongly stable c stationary point for mpcc strong stability refers to the local uniqueness existence and continuous dependence of a solution for each sufficiently small perturbed problem where perturbations up to second order are allowed this concept of strong stability was originally introduced by kojima for standard nonlinear optimization here its generalization to mpcc demands a sophisticated technique which takes the disjunctive properties of the solution set of mpcc into account

a smoothing method for mathematical programs with equilibrium constraints the mathematical program with equilibrium constraints mpec is an optimization problem with variational inequality constraints mpec problems include bilevel programming problems as a particular case and have a wide range of applications mpec problems with strongly monotone variational inequalities are considered in this paper they are transformed into an equivalent one level nonsmooth optimization problem then a sequence of smooth regular problems that progressively approximate the nonsmooth problem and that can be solved by standard available software for constrained optimization is introduced it is shown that the solutions stationary points of the approximate problems converge to a solution stationary point of the original mpec problem numerical results showing viability of the approach are reported

accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

a new class of truly consistent splitting schemes for incompressible flows a new class of splitting schemes for incompressible flows is introduced the new schemes are based on a weak form of the pressure poisson equation and at each time step only require to solve a set of helmholtz type equations for the velocity and a poisson equation in the weak form for the pressure just as pressure correction and velocity correction schemes however unlike pressure correction and velocity correction schemes the new splitting schemes are free of splitting errors and deliver full accuracy on the vorticity and the pressure

strong duality and kkt conditions in nonconvex optimization with a single equality constraint and geometric constraint some topological and geometric characterizations of strong duality for a non convex optimization problem under a single equality and geometric constraints are established in particular a hidden convexity of the conic hull of joint range of the pair of functions associated to the original problem is obtained applications to derive a characterization of the validity of kkt conditions without standard constraints qualification are also discussed it goes beyond the exact penalization technique several examples showing our results provide much more information than those appearing elsewhere are given finally the standard quadratic problem involving a non necessarily polyhedral cone is analyzed in detail

nondistorting flattening maps and the 3 d visualization of colon ct images considers a novel three dimensional 3 d visualization technique based on surface flattening for virtual colonoscopy such visualization methods could be important in virtual colonoscopy because they have the potential for noninvasively determining the presence of polyps and other pathologies further the authors demonstrate a method that presents a surface scan of the entire colon as a cine and affords the viewer the opportunity to examine each point on the surface without distortion the authors use certain angle preserving mappings from differential geometry to derive an explicit method for flattening surfaces obtained from 3 d colon computed tomography ct imagery indeed the authors describe a general method based on a discretization of the laplace beltrami operator for flattening a surface into the plane in a conformal manner from a triangulated surface representation of the colon the authors indicate how the procedure may be implemented using a finite element technique which takes into account special boundary conditions they also provide simple formulas that may be used in a real time cine to correct for distortion

stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications abstract we consider a class of optimization problems that is called a mathematical program with vanishing constraints mpvc for short this class has some similarities to mathematical programs with equilibrium constraints mpecs for short and typically violates standard constraint qualifications hence the well known karush kuhn tucker conditions do not provide necessary optimality criteria in order to obtain reasonable first order conditions under very weak assumptions we introduce several mpvc tailored constraint qualifications discuss their relation and prove an optimality condition which may be viewed as the counterpart of what is called m stationarity in the mpec field

two level method based on finite element and crank nicolson extrapolation for the time dependent navier stokes equations a fully discrete two level finite element method the two level method is presented for solving the two dimensional time dependent navier stokes problem the method requires a crank nicolson extrapolation solution u h tau 0 p h tau 0 on a spatial time coarse grid j h tau 0 and a backward euler solution u h tau p h tau on a space time fine grid j h tau the error estimates of optimal order of the discrete solution for the two level method are derived compared with the standard crank nicolson extrapolation method the one level method based on a space time fine grid j h tau the two level method is of the error estimates of the same order as the one level method in the h1 norm for velocity and the l2 norm for pressure however the two level method involves much less work than the one level method

a rotational velocity correction projection method for unsteady incompressible magnetohydrodynamics equations abstract this paper provides a rotational velocity correction projection method for the unsteady incompressible magnetohydrodynamics mhd equations in this method the electrical field variable e was eliminated in this way the gauss s law can be conserved the velocity variable u and the pressure field p are solved by a rotational velocity correction projection method the optimal error estimates of the l 2 norm will be given finally we shall present some numerical results to confirm our analysis it shows that our method is effective and can conserve the gauss s law very well

a new regularization method for mathematical programs with complementarity constraints with strong convergence properties mathematical programs with equilibrium or complementarity constraints mpecs form a difficult class of optimization problems the feasible set has a very special structure and violates most of the standard constraint qualifications therefore one typically applies specialized algorithms in order to solve mpecs one very prominent class of specialized algorithms are the regularization or relaxation methods the first regularization method for mpecs is due to scholtes siam j optim 11 2001 pp 918 936 but in the meantime there exist a number of different regularization schemes which try to relax the difficult constraints in different ways however almost all regularization methods converge to c stationary points only which is a very weak stationarity concept an exception is a recent method by kadrani dussault and benchakroun siam j optim 20 2009 pp 78 103 whose limit points are shown to be m stationary here we provide a new regularization method which also converges to m sta

defect correction finite element method for the stationary incompressible magnetohydrodynamics equation in this study we give the defect correction finite element method for the stationary incompressible mhd equation firstly the nonlinear mhd equation is solved with an artificial viscosity term then the numerical solution is improved on the same grid by a linearized defect correction technique then we give the numerical analysis including stability analysis and error analysis the numerical analysis proves that our method is stable and has an optimal convergence rate then we give some numerical results from the numerical results we can see that our method is efficient for solving the mhd equations

the coc algorithm part ii topological geometrical and generalized shape optimization abstract after outlining analytical methods for layout optimization and illustrating them with examples the coc algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members the numerical results obtained are shown to be in close agreement up to twelve significant digits with analytical results finally the problem of generalized shape optimization finding the best boundary topology and shape is discussed

dynamic time warping under pointwise shape context similarity measures are of fundamental importance in time series data mining dynamic time warping dtw is a quite popular measure because it handles time distortions well however dtw has an inherent shortcoming in that dtw can lead to pathological alignments between time series where a single point maps onto a large subsection of another time series to overcome this problem we propose a novel variant of dtw named sc dtw sc dtw employs shape context a rich local shape descriptor to replace the raw observed values considered by conventional dtw the main novelties of sc dtw are 1 it deeply explores both the numerical nature and shape nature of time series and 2 neighborhood information for each point is taken into account sc dtw can generate a more feature to feature alignment between time series and thus serves as a robust similarity measure we test the performance of sc dtw on ucr time series datasets using the one nearest neighbor 1nn classifier compared with other well established methods sc dtw provides better accuracy on 24 of 34 datasets

convergence analysis of three finite element iterative methods for the 2d 3d stationary incompressible magnetohydrodynamics abstract three finite element iterative methods are designed and analyzed for solving 2d 3d stationary incompressible magnetohydrodynamics mhd by a new technique strong uniqueness conditions for both stokes type iterative method iterative method i and newton iterative method iterative method ii are obtained which are weaker than the ones reported in open literature stability and optimal convergence rates for the above two methods are derived where the iterative method ii has an exponential convergent part with respect to iterative step m moreover oseen type iterative method iterative method iii is unconditionally stable and convergent under a uniqueness condition finally performance of the three proposed methods is investigated by numerical experiments

characterizing fj and kkt conditions in nonconvex mathematical programming with applications in this paper we analyze the fritz john and karush kuhn tucker kkt conditions for a g teaux differentiable nonconvex optimization problem with inequality constraints and a geometric constraint set the fritz john condition is characterized in terms of an alternative theorem which covers beyond standard situations while characterizations of kkt conditions without assuming constraints qualifications are related to strong duality of a suitable linear approximation of the given problem and the properties of its associated image mapping such characterizations are suitable for dealing with some problems in structural optimization where most of the known constraint qualifications fail in particular several examples are given showing the usefulness and optimality in a certain sense of our results which provide much more information than those including the mordukhovich normal cone or clarke s appearing elsewhere the case with a single inequality constraint is discussed in detail by establishing

unconditional stability and error estimates of the modified characteristics fems for the time dependent incompressible mhd equations abstract this paper focuses on the unconditional stability and convergence of characteristics type methods for the time dependent incompressible mhd equations for this purpose we introduce a new characteristics time discrete system the optimal error estimates in l 2 and h 1 norms for the typical modified characteristics finite element method unconditionally can be deduced while the whole previous works require certain time step restrictions some numerical experiments document performance of the characteristics type methods for the time dependent incompressible mhd equations

lipschitz and holder stability of optimization problems and generalized equations this paper studies stability aspects of solutions of parametric mathematical programs and generalized equations respectively with disjunctive constraints we present sufficient conditions that under some constraint qualifications ensuring metric subregularity of the constraint mapping continuity results of upper lipschitz and upper holder type respectively hold furthermore we apply the above results to parametric mathematical programs with equilibrium constraints and demonstrate how some classical results for the nonlinear programming problem can be recovered and even improved by our theory

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

critical sets in parametric optimization we deal with one parameter families of optimization problems in finite dimensions the constraints are both of equality and inequality type the concept of a generalized critical point g c point is introduced in particular every local minimum kuhn tucker point and point of fritz john type is a g c point under fairly weak even generic conditions we study the set consisting of all g c points due to the parameter the set is pieced together from one dimensional manifolds the points of can be divided into five characteristic types the subset of nondegenerate critical points first type is open and dense in nondegenerate means strict complementarity nondegeneracy of the corresponding quadratic form and linear independence of the gradients of binding constraints a nondegenerate critical point is completely characterized by means of four indices the change of these indices along is presented finally the kuhn tucker subset of is studied in more detail in particular in connection with the failure of the mangasarian fromowitz constraint qualification

mathematical programs with vanishing constraints optimality conditions and constraint qualifications we consider a difficult class of optimization problems that we call a mathematical program with vanishing constraints problems of this kind arise in various applications including optimal topology design problems of mechanical structures we show that some standard constraint qualifications like licq and mfcq usually do not hold at a local minimum of our program whereas the abadie constraint qualification is sometimes satisfied we also introduce a suitable modification of the standard abadie constraint qualification as well as a corresponding optimality condition and show that this modified constraint qualification holds under fairly mild assumptions we also discuss the relation between our class of optimization problems with vanishing constraints and a mathematical program with equilibrium constraints

an active set newton method for mathematical programs with complementarity constraints for a mathematical program with complementarity constraints mpcc we propose an active set newton method which has the property of local quadratic convergence under the mpcc linear independence constraint qualification mpcc licq and the standard second order sufficient condition sosc for optimality under mpcc licq this sosc is equivalent to the piecewise sosc on branches of mpcc which is weaker than the special mpcc sosc often employed in the literature the piecewise sosc is also more natural than mpcc sosc because unlike the latter it has an appropriate second order necessary condition as its counterpart in particular our assumptions for local quadratic convergence are weaker than those required by standard sqp when applied to mpcc and are equivalent to assumptions required by piecewise sqp for mpcc moreover each iteration of our method consists of solving a linear system of equations instead of a quadratic program some globalization issues of the local scheme are also discussed and illustrative examples and numerical experiments are presented

stationarity conditions and constraint qualifications for mathematical programs with switching constraints in optimal control switching structures demanding at most one control to be active at any time instance appear frequently discretizing such problems a so called mathematical program with switching constraints is obtained although these problems are related to other types of disjunctive programs like optimization problems with complementarity or vanishing constraints their inherent structure makes a separate consideration necessary since standard constraint qualifications are likely to fail at the feasible points of switching constrained optimization problems stationarity notions which are weaker than the associated karush kuhn tucker conditions need to be investigated in order to find applicable necessary optimality conditions furthermore appropriately tailored constraint qualifications need to be formulated in this paper we introduce suitable notions of weak mordukhovich and strong stationarity for mathematical programs with switching constraints and present some associated constraint qualifications our findings are exploited to state necessary optimality conditions for discretized optimal control problems with switching constraints furthermore we apply our results to optimization problems with either or constraints first a novel reformulation of such problems using switching constraints is presented second the derived surrogate problem is exploited to obtain necessary optimality conditions for the original program

how stringent is the linear independence assumption for mathematical programs with complementarity constraints the linear independence constraint qualifications licq plays an important role in the analysis of mathematical programs with complementarity constraints mpccs and is a vital ingredient to convergence analyses of sqp type or smoothing methods cf e g fukushima and pang 1999 luo et al 1996 scholtes and sta hr 1999 scholtes 2001 sta hr 2000 we will argue in this paper that licq is not a particularly stringent assumption for mpccs our arguments are based on an extension of jongen s 1977 genericity analysis to mpccs his definitions of nondegenerate critical points and regular programs extend naturally to mpccs and his genericity results generalize straightforwardly to mpccs in standard form an extension is not as straightforward for mpccs with the particular structure induced by lower level stationarity conditions for variational inequalities or optimization problems we show that licq remains a generic property for this class of mpccs

a mixed integer programming for robust truss topology optimization with stress constraints this paper presents a mixed integer programming mip formulation for robust topology optimization of trusses subjected to the stress constraints under the uncertain load a design dependent uncertainty model of the external load is proposed for dealing with the variation of truss topology in the course of optimization for a truss with the discrete member cross sectional areas it is shown that the robust topology optimization problem can be reduced to an mip problem which is solved globally numerical examples illustrate that the robust optimal topology of a truss depends on the magnitude of uncertainty

local stress constrained and slope constrained sand topology optimisation summary we study the alternative simultaneous analysis and design sand formulation of the local stress and slope constrained topology design problem it is demonstrated that a standard trust region lagrange newton sequential quadratic programming sqp type algorithm based in this case on strictly convex and separable approximate subproblems may converge to singular optima of the local stress constrained problem without having to resort to relaxation or perturbation techniques moreover due to the negation of the sensitivity analyses in sand the density and displacement variables are independent and the immense sparsity of the sand problem solutions to large scale problem instances may be obtained in a reasonable amount of computation time this article is protected by copyright all rights reserved

convergence properties of a regularization scheme for mathematical programs with complementarity constraints we study the convergence behavior of a sequence of stationary points of a parametric nlp which regularizes a mathematical program with equilibrium constraints mpec in the form of complementarity conditions accumulation points are feasible points of the mpec they are c stationary if the mpec linear independence constraint qualification holds they are m stationary if in addition an approaching subsequence satisfies second order necessary conditions and they are b stationary if in addition an upper level strict complementarity condition holds these results complement recent results of fukushima and pang convergence of a smoothing continuation method for mathematical programs with equilibrium constraints in ill posed variational problems and regularization techniques springer verlag new york 1999 we further show that every local minimizer of the mpec which satisfies the linear independence upper level strict complementarity and a second order optimality condition can be embedded into a locally unique piecewise smooth curve of local minimizers of the parametric nlp

the c index a new stability concept for quadratic programs with complementarity constraints we introduce nondegeneracy and the c index for c stationary points of a qpcc that is for a mathematical program with a quadratic objective function and linear complementarity constraints the c index characterizes the qualitative local behavior of a qpcc around a nondegenerate c stationary point the article focuses on the structure of the c stationary set of qpccs depending on a real parameter we show that for generic qpcc data the c index changes exactly at turning points of the c stationary set and that it changes by exactly one to illustrate this concept we introduce and analyze two homotopy methods for finding c stationary points numerical results illustrate that for randomly generated test problems the two homotopy methods very often identify b stationary points

characterization of strong stability for c stationary points in mpcc we study mathematical programs with complementarity constraints mpcc special focus will be on c stationary points under the linear independence constraint qualification we characterize strong stability of c stationary points in the sense of kojima by means of first and second order information of the defining functions it turns out that strong stability of c stationary points allows a possible degeneracy of bi active lagrange multipliers some relations to other stationarity concepts such as a m s and b stationarity are shortly discussed

automatic construction of correspondences for tubular surfaces statistical shape modeling is an established technique and is used for a variety of tasks in medical image processing such as image segmentation and analysis a challenging task in the construction of a shape model is establishing a good correspondence across the set of training shapes especially for shapes of cylindrical topology very little work has been done this paper describes an automatic method to obtain a correspondence for a set of cylindrical shapes the method starts from an initial correspondence which is provided by cylindrical parameterization the quality of the obtained correspondence measured in terms of the description length is then improved by deforming the parameterizations using cylindrical b spline deformations and by optimization of the spatial alignment of the shapes in order to allow efficient gradient guided optimization an analytic expression is provided for the gradient of this quality measure with respect to the parameters of the parameterization deformation and the spatial alignment a comparison is made between models obtained from the correspondences before and after the optimization the results show that in comparison with parameterization based correspondences this new method establishes correspondences that generate models with significantly increased performance in terms of reconstruction error generalization ability and specificity

sensitivity analysis for cone constrained optimization problems under the relaxed constraint qualifications we present the local sensitivity analysis for cone constrained optimization problems under the cq type conditions significantly weaker than those traditionally used in this context our basic sensitivity results are established under the first or second order sufficient optimality conditions combined with the estimate of the distance to the feasible set of the perturbed problem we demonstrate how such an estimate can be obtained under the assumptions weaker than robinson s cq and establish the corresponding sensitivity results finally we apply our results to sensitivity analysis and relaxation schemes for mathematical programs with complementarity constraints

on the existence uniqueness and finite element approximation of solutions of the equations of stationary incompressible magnetohydrodynamics the authors consider the equations of stationary incompressible magneto hydrodynamics posed in a bounded domain in three dimensions and treat the full coupled system of equations with inhomogeneous boundary conditions under certain conditions on the data they show that the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed they discuss a finite element discretization of the equations and prove an optimal estimate for the error of the approximate solution

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

on stability of the feasible set of a mathematical problem with complementarity problems the feasible set of mathematical programs with complementarity constraints mpcc is considered we discuss local stability of the feasible set with respect to perturbations up to first order of the defining functions here stability refers to homeomorphy invariance under small perturbations for stability we propose a kind of mangasarian fromovitz condition mfc and its stronger version smfc mfc is a natural constraint qualification for c stationarity and smfc is a generalization of the well known clarke s maximal rank condition it turns out that smfc implies local stability mfc and smfc coincide in the case where the number of complementarity constraints k equals the dimension of the state space n moreover the equivalence of mfc and smfc is also proven for the cases k 2 as well as under linear independence constraint qualification licq for mpcc

morphometric tools for landmark data geometry and biology 1 introduction 2 preliminaries 3 landmarks 4 distance measures 5 shape coordinates 6 principal axes of shape change for triangles 7 features of shape comparison 8 retrospect and prospect

convergence of gauge method for incompressible flow a new formulation a gauge formulation of the incompressible navier stokes equations in terms of an auxiliary field a and a gauge variable u a was proposed recently by e and liu this paper provides a theoretical analysis of their formulation and verifies the computational advantages we discuss the implicit gauge method which uses backward euler or crank nicolson in time discretization however the boundary conditions for the auxiliary field a are implemented explicitly vertical extrapolation the resulting momentum equation is decoupled from the kinematic equation and the computational cost is reduced to solving a standard heat and poisson equation moreover such explicit boundary conditions for the auxiliary field a will be shown to be unconditionally stable for stokes equations for the full nonlinear navier stokes equations the time stepping constraint is reduced to the standard cfl constraint t x c we also prove first order convergence of the gauge method when we use mac grids as our spatial discretization the optimal error estimate for the velocity field is also obtained

book review implicit functions and solution mappings a view from variational analysis second edition by a l dontchev and r t rockafellar springer new york 2014

velocity correction projection methods for incompressible flows we introduce and study a new class of projection methods namely the velocity correction methods in standard form and in rotational form for solving the unsteady incompressible navier stokes equations we show that the rotational form provides improved error estimates in terms of the h1 norm for the velocity and of the l2 norm for the pressure we also show that the class of fractional step methods introduced in s a orsag m israeli and m deville j sci comput 1 1986 pp 75 111 and k e karniadakis m israeli and s a orsag j comput phys 97 1991 pp 414 443 can be interpreted as the rotational form of our velocity correction methods thus to the best of our knowledge our results provide the first rigorous proof of stability and convergence of the methods in those papers we also emphasize that contrary to those of the above groups our formulations are set in the standard l2 setting and consequently they can be easily implemented by means of any variational approximation techniques in particular the finite element methods

critical solutions of nonlinear equations stability issues it is known that when the set of lagrange multipliers associated with a stationary point of a constrained optimization problem is not a singleton this set may contain so called critical multipliers this special subset of lagrange multipliers defines to a great extent stability pattern of the solution in question subject to parametric perturbations criticality of a lagrange multiplier can be equivalently characterized by the absence of the local lipschitzian error bound in terms of the natural residual of the optimality system in this work taking the view of criticality as that associated to the error bound we extend the concept to general nonlinear equations not necessarily with primal dual optimality structure among other things we show that while singular noncritical solutions of nonlinear equations can be expected to be stable only subject to some poor asymptotically thin classes of perturbations critical solutions can be stable under rich classes of perturbations this fact is quite remarkable considering that in the case of nonisolated solutions critical solutions usually form a thin subset within all the solutions we also note that the results for general equations lead to some new insights into the properties of critical lagrange multipliers i e solutions of equations with primal dual structure

elastic model based segmentation of 3 d neuroradiological data sets this paper presents a new technique for the automatic model based segmentation of three dimensional 3 d objects from volumetric image data the development closely follows the seminal work of taylor and cootes on active shape models but is based on a hierarchical parametric object description rather than a point distribution model the segmentation system includes both the building of statistical models and the automatic segmentation of new image data sets via a restricted elastic deformation of shape models geometric models are derived from a sample set of image data which have been segmented by experts the surfaces of these binary objects are converted into parametric surface representations which are normalized to get an invariant object centered coordinate system surface representations are expanded into series of spherical harmonics which provide parametric descriptions of object shapes it is shown that invariant object surface parametrization provides a good approximation to automatically determine object homology in terms of sets of corresponding sets of surface points gray level information near object boundaries is represented by 1 d intensity profiles normal to the surface considering automatic segmentation of brain structures as their driving application the authors choice of coordinates for object alignment was the well accepted stereotactic coordinate system major variation of object shapes around the mean shape also referred to as shape eigenmodes are calculated in shape parameter space rather than the feature space of point coordinates segmentation makes use of the object shape statistics by restricting possible elastic deformations into the range of the training shapes the mean shapes are initialized in a new data set by specifying the landmarks of the stereotactic coordinate system the model elastically deforms driven by the displacement forces across the object s surface which are generated by matching local intensity profiles elastical deformations are limited by setting bounds for the maximum variations in eigenmode space the technique has been applied to automatically segment left and right hippocampus thalamus putamen and globus pallidus from volumetric magnetic resonance scans taken from schizophrenia studies the results have been validated by comparison of automatic segmentation with the results obtained by interactive expert segmentation

a mixed finite element method with exactly divergence free velocities for incompressible magnetohydrodynamics abstract we introduce and analyze a mixed finite element method for the numerical discretization of a stationary incompressible magnetohydrodynamics problem in two and three dimensions the velocity field is discretized using divergence conforming brezzi douglas marini bdm elements and the magnetic field is approximated by curl conforming nedelec elements the h 1 continuity of the velocity field is enforced by a dg approach a central feature of the method is that it produces exactly divergence free velocity approximations and captures the strongest magnetic singularities we prove that the energy norm error is convergent in the mesh size in general lipschitz polyhedra under minimal regularity assumptions and derive nearly optimal a priori error estimates for the two dimensional case we present a comprehensive set of numerical experiments which indicate optimal convergence of the proposed method for two dimensional as well as three dimensional problems

on the time transformation of mixed integer optimal control problems using a consistent fixed integer control function nonlinear control systems with instantly changing dynamical behavior can be modeled by introducing an additional control function that is integer valued in contrast to a control function that is allowed to have continuous values the discretization of a mixed integer optimal control problem miocp leads to a non differentiable optimization problem and the non differentiability is caused by the integer values the paper is about a time transformation method that is used to transform a miocp with integer dependent constraints into an ordinary optimal control problem differentiability is achieved by replacing a variable integer control function with a fixed integer control function and a variable time allows to change the sequence of active integer values in contrast to other contributions so called control consistent fixed integer control functions are taken into account here it is shown that these control consistent fixed integer control functions allow a better accuracy in the resulting trajectories in particular in the computed switching times the method is verified on analytical and numerical examples

mpcc critical point theory we study mathematical programs with complementarity constraints mpcc from a topological point of view special focus will be on c stationary points under the linear independence constraint qualification licq we derive an equivariant morse lemma at nondegenerate c stationary points then two basic theorems from morse theory deformation theorem and cell attachment theorem are proved outside the c stationary point set continuous deformation of lower level sets can be performed as a consequence the topological data such as the number of connected components then remain invariant however when passing a c stationary level the topology of the lower level set changes via the attachment of a q dimensional cell the dimension q equals the stationary c index of the nondegenerate c stationary point the stationary c index depends on both the restricted hessian of the lagrangian and the lagrange multipliers related to biactive complementarity constraints finally some relations with other stationarity concepts such as w a m s and b stationarity are discussed

genus zero surface conformal mapping and its application to brain surface mapping we developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one forms for surfaces with or without boundaries gu and yau 2002 gu and yau 2003 for genus zero surfaces our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map in this paper we apply the algorithm to the cortical surface matching problem we use a mesh structure to represent the brain surface further constraints are added to ensure that the conformal map is unique empirical tests on magnetic resonance imaging mri data show that the mappings preserve angular relationships are stable in mris acquired at different times and are robust to differences in data triangulation and resolution compared with other brain surface conformal mapping algorithms our algorithm is more stable and has good extensibility