goal programming for decision making an overview of the current state of the art there have been significant advances in the theory of goal programming gp in recent years particularly in the area of intelligent modelling and solution analysis the intention of this paper is to provide an overview of these developments to detail and assess the current state of the art in the subject and to highlight areas which seem promising for future research modelling techniques such as detection and restoration of pareto efficiency normalisation redundancy checking and non standard utility function modelling are overviewed the connection between gp and other multi objective programming techniques as well as a utility interpretation of gp are examined the rationality of ranking multi criteria decision making techniques and of placing gp in such a ranking is discussed

the long step method of analytic centers for fractional problems we develop a long step surface following version of the method of analytic centers for the fractional linear problem min t 0 t 0 b x a x eh b x ek x eg whereh is a closed convex domain k is a convex cone contained in the recessive cone ofh g is a convex domain andb a are affine mappings tracing a two dimensional surface of analytic centers rather than the usual path of centers allows to skip the initial centering phase of the path following scheme the proposed long step policy of tracing the surface fits the best known overall polynomial time complexity bounds for the method and at the same time seems to be more attractive computationally than the short step policy which was previously the only one giving good complexity bounds

an algorithm using the finite volume element method and its splitting extrapolation this paper is to present a new efficient algorithm by using the finite volume element method and its splitting extrapolation this method combines the local conservation property of the finite volume element method and the advantages of splitting extrapolation such as a high order of accuracy a high degree of parallelism less computational complexity and more flexibility than a richardson extrapolation because the splitting extrapolation formulas only require us to solve a set of smaller discrete subproblems on different coarser grids in parallel instead of on the globally fine grid a large scale multidimensional problem is turned into a set of smaller discrete subproblems additionally this method is efficient for solving interface problems if we regard the interfaces of the problems as the interfaces of the initial domain decomposition

on polynomiality of the method of analytic centers for fractional problems we establish polynomial time convergence of the method of analytic centers for the fractional programming problemt min x g tb x a x k whereg n is a closed and bounded convex domain k m is a closed convex cone anda x g n b x g k are regular enough say affine mappings

inflating a flat toroidal membrane abstract a flat toroidal geometry composed of a stack of two flat annular membranes bonded together at the inner and outer boundaries equators is proposed the finite inflation mechanics of the composite membrane under uniform internal pressure is considered the membranes are assumed to be identical homogeneous and isotropic solids described by the gent hyperelastic model with a relaxed strain energy density function the variational inflation mechanics problem yields the governing equations and boundary conditions which are recast as a nonlinear two point boundary value problem in a suitable form for efficient computation the effects of the inflation pressure and material properties on the state of stretch and geometry of the inflated toroidal membrane are obtained which exhibit a number of desirable features the phenomenon of wrinkling instability is observed near the outer equator of the torus at low pressures in spite of a positive gaussian curvature which is exactly opposite to the behavior observed in a curved torus wrinkling at the inner equator at high pressure semi analytical expressions of the cauchy stress resultants are obtained which match well with the numerical computations further the limit point instability pressure of the toroidal membrane is shown to have a remarkable power law dependence on a geometric parameter of the uninflated flat torus and the material chain extensibility parameter involving two universal constants

hyperbolic polynomials and interior point methods for convex programming hyperbolic polynomials have their origins in partial differential equations we show in this paper that they have applications in interior point methods for convex programming each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone we give an explicit representation of this cone in terms of polynomial inequalities the function fx log px is a logarithmically homogeneous self concordant barrier function for the hyperbolicity cone with barrier parameter equal to the degree of p the function fx possesses striking additional properties that are useful in designing long step interior point methods for example we show that the long step primal potential reduction methods of nesterov and todd and the surface following methods of nesterov and nemirovskii extend to hyperbolic barrier functions we also show that there exists a hyperbolic barrier function on every homogeneous cone

generalized goal programming polynomial methods and applications in this paper we address a general goal programming problem with linear objectives convex constraints and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets in particular classical linear goal programming problems as well as several models in location and regression analysis are modeled within this framework

a new approach to the numerical solution of weakly singular volterra integral equations we consider linear weakly singular volterra integral equations of the second kind with kernels of the form k x v x v k x v 0 1 or k x v log x v k x v k x v being a smooth function the solutions of such equations may exhibit a singular behaviour in the neighbourhood of the initial point of the interval of integration by a transformation of the unknown function we obtain an equation which is still weakly singular but whose solution is as smooth as we like this resulting equation is then solved by standard product integration methods

the general one center location problem the general one center location problem deals with the location of a point in a real normed space x in order to minimize an objective function g which depends on the distances to a finite number of centers and on initial costs the function g is defined by g x c1 w1 x a1 cn wn x an where a1 an are n given points in x w1 wn are positive numbers c1 cn are nonnegative initial costs and is a monotone norm on n a geometrical description of the set of optimal solutions to the problem minx x g x is provided the peculiar role of the minisum problem where is the l1 norm is emphasized and the minimax problem where is the lx norm is used to illustrate the general geometrical description

uniform approximation to fractional derivatives of functions of algebraic singularity fractional derivative d qf x 0 1 with g x being a well behaved function we propose a quadrature method for uniformly approximating d q x ag x the present method consists of interpolating g x at abscissae in 0 1 by a finite sum of chebyshev polynomials it is shown that the use of the lower endpoint x 0 as an abscissa is essential for the uniform approximation namely to bound the approximation errors independently of x 0 1 numerical examples demonstrate the performance of the present method

a hierarchy of plate models derived from nonlinear elasticity by gamma convergence we derive a hierarchy of plate models from three dimensional nonlinear elasticity by convergence what distinguishes the different limit models is the scaling of the elastic energy per unit volume h where h is the thickness of the plate this is in turn related to the strength of the applied force h membrane theory derived earlier by le dret and raoult corresponds to 0 nonlinear bending theory to 2 von karman theory to 3 4 and linearized vk theory to 3 intermediate values of lead to certain theories with constraints a key ingredient in the proof is a generalization to higher derivatives of our rigidity result 29 which states that for maps v 0 1 3 3 the l2 distance of v from a single rotation is bounded by a multiple of the l2 distance from the set so 3 of all rotations

on the von neumann economic growth problem we study the complexity of the von neumann economic growth problem gamma ast max gamma mid exists y ne 0 y ge 0 b gamma ay ge 0 where a and b are given two nonnegative and rational m n matrices and a has no all zero column let the binary data length of a and b be l we develop an interior point algorithm to generate a i such that 2 1 i in om nl minm nt iterations where each iteration solves a system of m n linear equations

new numerical method for two dimensional partially wrinkled membranes based on the introduction of a nonnegative adjustable parameter into poisson s ratio a new numerical method is proposed to solve numerically the partially wrinkled membrane problems with arbitrary complex shapes three fundamental issues in this new method are addressed first a nonnegative adjustable parameter is introduced into the constitutive law automatically representing unwrinkled taut and wrinkled states of a membrane second a parametric variational principle is developed for the new membrane model third by the variational principle the original membrane problem is converted to a nonlinear mathematical programming problem the variational principle and the mathematical programming formulation lay a foundation for efficient numerical analysis of wrinkled membrane structures using finite element discretization three typical examples are given to show the effectiveness of this method

on the self concordance of the universal barrier function let k be a regular convex cone in hbox bbb r n and let f x be its universal barrier function let d kf x h ldots h be the k th order directional derivative at the point x in k 0 and direction h in hbox bbb r n we show that for every m ge3 there exists a constant c m 0 depending only on m such that d mf x h ldots h le c m d 2f x h h m 2 for m 3 this is the self concordance inequality of nesterov and nemirovskii our proof uses a powerful recent result of bourgain

a quadratically convergent polynomial algorithm for solving entropy optimization problems a potential reduction algorithm is developed for solving entropy optimization problems it is shown that the algorithm generates an epsilon optimal solution within at most o sqrt n log epsilon iterations where as usual n is the number of nonnegative variables and each iteration solves a system of linear equations under a computable criterion the algorithm is tuned to the pure newton method in a manner that leads to quadratic convergence while maintaining primal feasibility at each step a stopping criterion is derived which ensures that the objective function approaches its optimal value within any prescribed tolerance this applies for all entropy optimization problems having interior optimal solutions

a new operational method to solve abel s and generalized abel s integral equations abstract based on jacobi polynomials an operational method is proposed to solve the generalized abel s integral equations a class of singular integral equations these equations appear in various fields of science such as physics astrophysics solid mechanics scattering theory spectroscopy stereology elasticity theory and plasma physics to solve the abel s singular integral equations a fast algorithm is used for simplifying the problem under study the laplace transform and jacobi collocation methods are merged and thus a novel approach is presented some theorems are given and established to theoretically support the computational simplifications which reduce costs also a new procedure for estimating the absolute error of the proposed method is introduced in order to show the efficiency and accuracy of the proposed method some numerical results are provided it is found that the proposed method has lesser computational size compared to other common methods such as adomian decomposition homotopy perturbation block pulse function mid point trapezoidal quadrature and product integration it is further found that the absolute errors are almost constant in the studied interval

multi parameter surfaces of analytic centers and long step surface following interior point methods we develop a long step polynomial time version of the method of analytic centers for non linear convex problems the method traces a multi parameter surface of analytic centers rather than the usual path which allows to handle cases with noncentered and possibly infeasible starting point

instability investigation on fluid loaded pre stretched cylindrical membranes this paper discusses the evaluation of instabilities on the quasi static equilibrium path of fluid loaded pre stretched cylindrical membranes and the switching to a secondary branch at a bifurcation point the membrane is represented by only the in plane stress components for which an incompressible isotropic hyperelastic material model is assumed the free inflation problem yields governing equations and boundary conditions which are discretized by finite differences and solved by a newton raphson method an incremental arclength cubic extrapolation method is used to find generalized equilibrium paths with different parametrizations limit points and bifurcation points are observed on the equilibrium path when fluid level is seen as the controlling parameter an eigen mode injection method is employed to switch to a secondary equilibrium branch at the bifurcation point a limit point with respect to fluid level is observed for a partially filled membrane when the aspect ratio length radius is high whereas for smaller aspect ratios the limit point with respect to fluid level is observed at over filling pre stretch is observed to have a stiffening effect in the pre limit zone and a softening effect in the post limit zone

a convenient technique for solving linear and nonlinear abel integral equations by the adomian decomposition method abstract in this paper linear and nonlinear abel integral equations are transformed in such a manner that the adomian decomposition method can be applied some examples with closed form solutions are studied in detail to further illustrate the proposed technique and the results obtained indicate this approach is indeed practical and efficient

contact analysis of cable networks by using second order cone programming a method based on mathematical programming is proposed for large deformation and contact analysis of cable networks by explicitly considering these nonsmooth behaviors we formulate the linear complementarity problems over symmetric cones under some practically acceptable assumptions we also present the equivalent second order cone programming socp problems which can be regarded as the minimization problem of total potential energy and complementary energy with the subsidiary constraints on the displacements and contact forces respectively by solving the presented socp problems by using the primal dual interior point method the equilibrium configurations and internal forces of several cable networks are obtained without any assumptions on stress states and contact conditions

equilibrium shapes of inflated inextensible membranes this paper proposes an effective method for directly determining the final equilibrium shapes of closed inextensible membranes subjected to internal pressures with reference to new high performance textile materials we assume that the mechanical response of a fabric membrane can be accurately represented by regarding it as a two state material in the active state the membrane is subject to tensile stresses and is virtually inextensible vice versa in the passive state it is unable to sustain any compressive stress so it contracts freely equilibrium of the membrane in the final configuration is enforced by recourse to the minimum total potential energy principle the lagrange multipliers method is used to solve the minimum problem by accounting for the aforesaid nonlinear constitutive law the set of governing equations is solved for the unknown coordinates of the equilibrium surface points closed form solutions are obtained for fully wrinkled cylindrical and axisymmetric membranes under homogeneous boundary conditions while a simple iterative procedure is used to numerically solve cases of axisymmetric membranes under various inhomogeneous boundary conditions the soundness of the proposed method is verified by comparing the results with solutions available in the literature

cone free primal dual path following and potential reduction polynomial time interior point methods we present a framework for designing and analyzing primal dual interior point methods for convex optimization we assume that a self concordant barrier for the convex domain of interest and the legendre transformation of the barrier are both available to us we directly apply the theory and techniques of interior point methods to the given good formulation of the problem as is without a conic reformulation using the very usual primal central path concept and a less usual version of a dual path concept we show that many of the advantages of the primal dual interior point techniques are available to us in this framework and therefore they are not intrinsically tied to the conic reformulation and the logarithmic homogeneity of the underlying barrier function

localization in single facility location abstract a well known localization theorem in continuous single facility location of wendell and hurter states that any weber problem in the plane in which all norms are identical admits an optimal solution within the convex hull of the destination points in this paper it is shown that this result fails for general norms as soon as the dimension is at least three a new localization theorem is then proposed that is valid under very general conditions this makes it possible to consider most unconstrained single facility location problems as constrained problems it is indicated how to construct an easily implemented form of such constraints

product integration for volterra integral equations of the second kind with weakly singular kernels we introduce a new numerical approach for solving volterra integral equations of the second kind when the kernel contains a mild singularity we give a convergence result we also present numerical examples which show the performance and efficiency of our method

convergence analysis of the jacobi collocation method for nonlinear weakly singular volterra integral equations in this work we present an efficient spectral collocation method for numerical solution of a class of nonlinear weakly singular volterra integral equations this type of equations typically has a singular behavior at the left endpoint of the interval of integration for overcoming this non smooth behavior we apply the jacobi collocation method the convergence analysis of the proposed method is investigated in the l and the weighted l2 norms and the results of several numerical experiments are presented which support the theoretical results the computed results are compared wherever possible with those already available in the literature

wrinkles as the result of compressive stresses in an annular thin film it is well known that an elastic sheet loaded in tension will wrinkle and that the length scale of the wrinkles tends to 0 with vanishing thickness of the sheet cerda and mahadevan phys rev lett 90 074302 2003 we give the first mathematically rigorous analysis of such a problem since our methods require an explicit understanding of the underlying convex relaxed problem we focus on the wrinkling of an annular sheet loaded in the radial direction davidovitch et al proc natl acad sci 108 2011 18227 our main achievement is identification of the scaling law of the minimum energy as the thickness of the sheet tends to 0 this requires proving an upper bound and a lower bound that scale the same way we prove both bounds first in a simplified kirchhoff love setting and then in the nonlinear three dimensional setting to obtain the optimal upper bound we need to adjust a naive construction one family of wrinkles superimposed on a planar deformation by introducing a cascade of wrinkles the lower bound is more subtle since it must be ansatz free 2014 wiley periodicals inc

mechanical quadrature methods and their extrapolation for solving first kind abel integral equations this paper presents high accuracy mechanical quadrature methods for solving first kind abel integral equations to avoid the ill posedness of problem the first kind abel integral equation is transformed to the second kind volterra integral equation with a continuous kernel and a smooth right hand side term expressed by weakly singular integrals by using periodization method and modified trapezoidal integration rule not only high accuracy approximation of the kernel and the right hand side term can be easily computed but also two quadrature algorithms for solving first kind abel integral equations are proposed which have the high accuracy o h 2 and asymptotic expansion of the errors then by means of richardson extrapolation an approximation with higher accuracy order o h 3 is obtained moreover an a posteriori error estimate for the algorithms is derived some numerical results show the efficiency of our methods

the modeling and numerical analysis of wrinkled membranes in this paper three fundamental issues regarding modeling and analysis of wrinkled membranes are addressed first a new membrane model with viable young s modulus and poisson s ratio is proposed which physically characterizes stress relaxation phenomena in membrane wrinkling and expresses taut wrinkled and slack states of a membrane in a systematic manner second a parametric variational principle is developed for the new membrane model third by the variational principle the original membrane problem is converted to a non linear complementarity problem in mathematical programming a parametric finite element discretization and a smoothing newton method are then used for numerical solution the proposed membrane model and numerical method are capable of delivering convergent results for membranes with a mixture of wrinkled and slack regions without iteration of membrane stresses three numerical examples are provided

monotonicity properties of norms abstract we consider several properties that might be described as monotonicity or absoluteness that a norm may or may not have and give a complete set of implications among them we also consider some related hadamard product inequalities under various normalizations

a unified successive pseudoconvex approximation framework in this paper we propose a successive pseudoconvex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems the stationary points are obtained by solving a sequence of successively refined approximate problems each of which is much easier to solve than the original problem to achieve convergence the approximate problem only needs to exhibit a weak form of convexity namely pseudoconvexity we show that the proposed framework not only includes as special cases a number of existing methods for example the gradient method and the jacobi algorithm but also leads to new algorithms that enjoy easier implementation and faster convergence speed we also propose a novel line search method for nondifferentiable optimization problems which is carried out over a properly constructed differentiable function with the benefit of a simplified implementation as compared to the state of the art line search techniques that directly operate on the original nondifferentiable objective function the advantages of the proposed algorithm are shown both theoretically and numerically by several example applications namely multi input multi output mimo broadcast channel capacity computation energy efficiency maximization in massive mimo systems and ell 1 regularized least square problems in sparse signal recovery

a simple computer implementation of membrane wrinkle behaviour via a projection technique a simple computer implementation of membrane wrinkle behaviour is presented within the classical elastic plane stress constitutive model in the present method a projection technique is utilized for modelling of the wrinkle mechanisms in which the total strains in wrinkled membranes are decomposed into elastic and zero strain energy parts and a projection matrix that extracts the elastic parts from the total strains is derived the resulting modified elasticity matrix that represents the stress strain relations in wrinkled membranes is thus obtained as product of the classical elasticity matrix and the projection matrix the modified elasticity matrix is straightforward to implement within the context of the finite element method numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed method copyright 2007 john wiley sons ltd

an interior point method for fractional programs with convex constraints we present an interior point method for a class of fractional programs with convex constraints the proposed algorithm converges at a polynomial rate similarly as in the case of a convex problem even though fractional programs are only pseudo convex here the rate of convergence is measured in terms of the area of two dimensional convex setsck containing the origin and certain projections of the optimal points and the area ofck is reduced by a constant factorc 1 at each iteration the factorc depends only on the self concordance parameter of a barrier function associated with the feasible set we present an outline of a practical implementation of the proposed method and we report results of some preliminary numerical experiments

long step strategies in interior point primal dual methods in this paper we analyze from a unique point of view the behavior of path following and primal dual potential reduction methods on nonlinear conic problems we demonstrate that most interior point methods with o root n ln 1 epsilon efficiency estimate can be considered as different strategies of minimizing a convex primal dual potential function in an extended primal dual space their efficiency estimate is a direct consequence of large local norm of the gradient of the potential function along a central path it is shown that the neighborhood of this path is a region of the fastest decrease of the potential therefore the long step path following methods are in a sense the best potential reduction strategies we present three examples of such long step strategies we prove also an efficiency estimate for a pure primal dual potential reduction method which can be considered as an implementation of a penalty strategy based on a functional proximity measure using the convex primal dual potential we prove efficiency estimates for karmarkar type and dikin type methods as applied to a homogeneous reformulation of the initial primal dual problem

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

an efficient algorithm for minimizing a sum of euclidean norms with applications in recent years rich theories on polynomial time interior point algorithms have been developed these theories and algorithms can be applied to many nonlinear optimization problems to yield better complexity results for various applications in this paper the problem of minimizing a sum of euclidean norms is studied this problem is convex but not everywhere differentiable by transforming the problem into a standard convex programming problem in conic form we show that an epsilon optimal solution can be computed efficiently using interior point algorithms as applications to this problem polynomial time algorithms are derived for the euclidean single facility location problem the euclidean multifacility location problem and the shortest network under a given tree topology in particular by solving the newton equation in linear time using em gaussian elimination on leaves of a tree we present an algorithm which computes an epsilon optimal solution to the shortest network under a given full steiner topology interconnecting n regular points in o n sqrt n log bar c epsilon log n arithmetic operations where bar c is the largest pairwise distance among the given points the previous best known result on this problem is a graphical algorithm which requires o n2 arithmetic operations under certain conditions

reconstruction of exponentially rate of convergence to legendre collocation solution of a class of fractional integro differential equations in this paper legendre collocation method an easy to use variant of the spectral methods for the numerical solution of a class of fractional integro differential equations fide s is researched in order to obtain high order accuracy for the approximation the integral term in the resulting equation is approximated by using legendre gauss quadrature formula an efficient convergence analysis of the proposed method is given and rate of convergence is established in the l 2 norm due to the fact that the solutions of fide s usually have a weak singularity at origin we use a variable transformation to change the original equation into a new equation with a smooth solution we prove that after this regularization technique numerical solution of the new equation by adopting the legendre collocation method has exponentially rate of convergence numerical results are presented which clarify the high accuracy of the proposed method

an interior point method for minimizing the maximum eigenvalue of a linear combination of matrices we consider the problem of finding lambda opt mathop inf limits x in r m lambda max a 0 sum limits i 1 m x i a i 1 and an optimal solution xopt if it exists here the a i are given symmetric matrices in ir n n for 0 i m and max a is the largest eigenvalue of a matrix a problem 1 can be rewritten as a convex differentiable problem with a positive definite constraint positive definiteness can easily be verified numerically via cholesky decomposition moreover the cone of positive definite matrices a is characterized by the domain of the smooth convex barrier function log det a

anisotropic membrane wrinkling theory and analysis abstract a complete theory of wrinkling of anisotropic elastic membranes is presented based on the notion of relaxed energy function the theory is obtained as a particular case of a general theory of saturated elasticity it is shown that when any given hyperelastic constitutive law is supplemented with a saturation condition the right cauchy green strain tensor abides by an additive decomposition law governed by a normality rule for the case of wrinkling these results are implemented into a numerical procedure and examples are presented

primal dual symmetry and scale invariance of interior point algorithms for convex optimization we present a definition of symmetric primal dual algorithms for convex optimization problems expressed in the conic form after describing a generalization of the space approach for such optimization problems we show that a symmetric space approach can be developed for a convex optimization problem in the conic form if and only if the underlying cone is homogeneous and self dual we provide an alternative definition of self scaled barriers and then conclude with a discussion of the scalings of the variables which keep the underlying convex cone invariant

duality theorem for a generalized fermat weber problem the classical fermat weber problem is to minimize the sum of the distances from a point in a plane tok given points in the plane this problem was generalized by witzgall ton dimensional space and to allow for a general norm not necessarily symmetric he found a dual for this problem the authors generalize this result further by proving a duality theorem which includes as special cases a great variety of choices of norms in the terms of the fermat weber sum the theorem is proved by applying a general duality theorem of rockafellar as applications a dual is found for the multi facility location problem and a nonlinear dual is obtained for a linear programming problem with a priori bounds for the variables when the norms concerned are continuously differentiable formulas are obtained for retrieving the solution for each primal problem from the solution of its dual

a novel variational algorithmic formulation for wrinkling at finite strains based on energy minimization application to mesh adaption this paper is concerned with an efficient novel algorithmic formulation for wrinkling at finite strains in contrast to previously published numerical implementations the advocated method is fully variational more precisely the parameters describing wrinkles or slacks together with the unknown deformation mapping are computed jointly by minimizing the potential energy of the considered mechanical system furthermore the wrinkling criteria are naturally included within the presented variational framework the proposed method allows to employ three dimensional constitutive models without any additional modification i e a projection in plane stress space is not required analogously to the wrinkling parameters the non vanishing out of plane component of the strain tensor results conveniently from relaxing the respective helmholtz energy of the membrane the proposed framework is very general and does not rely on any assumption regarding the symmetry of the material i e arbitrary anisotropic hyperelastic models can be consistently taken into account the advantages associated with such a variational method are manifold for instance it opens up the possibility of applying standard optimization algorithms to the numerical implementation this is especially important for highly non linear or singular problems such as wrinkling on the other hand minimization principles provide a suitable basis for a posteriori error estimation and thus for adaptive finite element formulations as a prototype a variational error indicator leading to an efficient h adaption for wrinkling is briefly discussed the performance of the wrinkling approach is demonstrated by selected finite element analyses

incremental stresses in loaded orthotropic circular membrane tubes i theory abstract starting from the equations of general elastic nonlinear membrane theory in intrinsic form the equations governing the incremental state of stress in an orthotropic circular membrane tube are derived and discussed the tube is initially subjected to uniform internal pressure and to longitudinal extension which lead to large homogeneous deformation then some changes in loading and or geometry are considered e g an additional load is applied the shape of the boundary is changed or a slit is formed in the membrane these changes are regarded as small perturbations on the initial homogeneous state of stress the general form as well as some simplified forms of the equations are presented leading finally to a set of two equations in terms of two scalar potential functions two different variational formulations for the problem are also presented each of which may serve as a basis for numerical treatment

inflation of nonlinearly deformed annular elastic membranes abstract the inflation of an isotropic nonlinear elastic membrane by means of a volume independent hydrostatic pressure is studied in particular we consider annular membranes which on the inner boundary have been subjected to an axial twist and a displacement normal to the plane of the membrane with the outer boundary fixed a direct two dimensional approach is adopted and by introducing a relaxed strain energy function the occurrence of wrinkled solutions is considered the governing equations are found to reduce to a system of first order differential equations which are then solved numerically for a mooney rivlin material over a range of boundary value problems

a finite element splitting extrapolation for second order hyperbolic equations splitting extrapolation is an efficient technique for solving large scale scientific and engineering problems in parallel this article discusses a finite element splitting extrapolation for second order hyperbolic equations with time dependent coefficients this method possesses a higher degree of parallelism less computational complexity and more flexibility than richardson extrapolation while achieving the same accuracy by means of domain decomposition and isoparametric mapping some grid parameters are chosen according to the problem the multiparameter asymptotic expansion of the d quadratic finite element error is also established the splitting extrapolation formulas are developed from this expansion an approximation with higher accuracy on a globally fine grid can be computed by solving a set of smaller discrete subproblems on different coarser grids in parallel some a posteriori error estimates are also provided numerical examples show that this method is efficient for solving discontinuous problems and nonlinear hyperbolic equations

elastic surface substrate interactions a theory for three dimensional finite deformations of elastic solids with conforming elastic films attached to their bounding surfaces is described the gurtin murdoch theory incorporating elastic resistance of the film to strain is generalized to account for the effects of intrinsic flexural resistance this modification yields a model that can be used to describe equilibrium deformations in the presence of compressive surface stress fields an associated variational theory is given and material symmetry considerations are discussed the theory is illustrated by examples

a generalization of discrete gronwall inequality and its application to weakly singular volterra integral equation of the second kind this paper presents a new discrete gronwall inequality using the inequality we prove convergence and error estimate of the numerical solutions of the second weakly singular volterra integral equation where discrete equation is derived by novot s quadrature formula

an efficient algorithm for minimizing a sum of p norms we study the problem of minimizing a sum of p norms where p is a fixed real number in the interval 1 infty several practical algorithms have been proposed to solve this problem however none of them has a known polynomial time complexity in this paper we transform the problem into standard conic form unlike those in most convex optimization problems the cone for the p norm problem is not self dual unless p 2 nevertheless we are able to construct two logarithmically homogeneous self concordant barrier functions for this problem the barrier parameter of the first barrier function does not depend on p the barrier parameter of the second barrier function increases with p using both barrier functions we present a primal dual potential reduction algorithm to compute an epsilon optimal solution in polynomial time that is independent of p computational experiences with a matlab implementation are also reported

dual gauge programs with applications to quadratic programming and the minimum norm problem a gauge functionf is a nonnegative convex function that is positively homogeneous and satisfiesf 0 0 norms and pseudonorms are specific instances of a gauge function this paper presents a gauge duality theory for a gauge program which is the problem of minimizing the value of a gauge functionf over a convex set the gauge dual program is also a gauge program unlike the standard lagrange dual we present sufficient conditions onf that ensure the existence of optimal solutions to the gauge program and its dual with no duality gap these sufficient conditions are relatively weak and are easy to verify and are independent of any qualifications on the constraints the theory is applied to a class of convex quadratic programs and to the minimuml p norm problem the gauge dual program is shown to provide a smaller duality than the standard dual in a certain sense discussed in the text

differential equation for the amplitude of wrinkles introduction t he renewed interest in the phenomenonof wrinkling of membranes fueled by applications to the aerospace industry has spurred considerable activity on both the theoretical and computational aspectsof the subject althoughthe wrinklingphenomenonis known to be a case of shell buckling it seems unwise to utilize this knowledge in actual computations because treating the membrane as a shell with a vanishinglysmall thickness leads to the frustrating effects of numerical instability there exist on the other hand techniques based on themembrane theory alone that permit us to obtain with relative ease and numerical robustness not only the extent of thewrinkledzones but also the eldof directionsof thewrinkles 1i4 all that is needed therefore is a means for calculating the amplitude and wavelength of the wrinkles in an already known wrinkled domain in this note we derive an ordinary differential equation whose solution delivers such information for clarity of the presentation the equation is obtained under a number of simplifying assumptions mostly involving the smallness of the deformations however the method is straightforwardlyextendable to the general case our guiding principle has been to keep only those aspects of the model that are clearly determinant of the result while leaving all other aspects for future re nement we believe that this philosophy will serve to highlight the essential features rather than the technicalities of the proposedequation note that even under a geometrically andmaterially linear regime the resultingdifferentialequation is highly nonlinear the physical reason for this nonlinearityis to be foundin that becausewrinklingentailsno stress in thedirectionperpendicular to the wrinkles there exists a severe constraint between the wavelength and amplitude of the wrinkles this can be phrased intuitively as follows for a given amount of wrinkling strain the larger the number of wrinkles the smaller their amplitude to the best of our knowledge the only attempt in a direction similar to the one proposed herein is due to wong and pellegrino in their work these authors present a model basedmainly on the particular case of shearing of a rectangular panel their results are very valuable and will be used here as a benchmark for validation purposes

geometrical properties of the fermat weber problem abstract this paper is devoted to the fermat weber problem with mixed gauges in order to take into account nonsymmetric distances a geometrical description of the set of solutions is obtained then the concept of metric hull is defined general sufficient conditions are given such that the metric hull of existing facilities intersects the set of optimal locations particularly it is shown that an optimal location can be found in the metric hull in dimension two whatever the gauges are and in dimension n with the rectilinear norm the connection between metric hull convex hull and octagonal hull is studied

optimal expected distance separating halfspace one recently proposed criterion to separate two data sets in discriminant analysis is to use a hyperplane which minimizes the sum of distances to it from all the misclassified data points here all distances are supposed to be measured by way of some fixed norm while misclassification means lying in the wrong halfspace in this paper we study the problem of determining such an optimal halfspace when points are distributed according to an arbitrary random vector x in rd in the unconstrained case in dimension d we prove that any optimal separating halfspace always balances the misclassified points moreover under polyhedrality assumptions on the support of x there always exists an optimal separating halfspace passing through d affinely independent points these results extend in a natural way when different norms or a fixed gauge are used to measure distances and we allow constraints modeling that certain points are forced to be correctly classified

an interior point method for generalized linear fractional programming we develop an interior point polynomial time algorithm for a generalized linear fractional problem the latter problem can be regarded as a nonpolyhedral extension of the usual linear fractional programming typical example which is of interest for control theory is the minimization of the generalized eigenvalue of a pair of symmetric matrices linearly depending on the decision variables

how to compute least infeasible flows it is well known how to use maximum flow to decide when a flow problem with demands lower bounds and upper bounds is infeasible less well known is how to compute a flow that is least infeasible this paper considers many possible ways to define least infeasible and shows how to compute optimal flows for each definition for each definition it also gives a dual characterization in terms of cuts a polynomial routine for recognizing that type of least infeasible flow and relates that definition to dual cut canceling min cost flow network algorithms

tension field theory a general theory of the tension field is developed for application to the analysis of wrinkling in isotropic elastic membranes undergoing finite deformations the principal contribution is a partial differential equation describing a geometrical property of tension trajectories this is one of a system of two equations which describes the state of stress independently of the deformation this system is strongly elliptic at any stable solution whereas the deformation is described by a system of parabolic type controllable solutions i e those states that can be maintained in any isotropic elastic material by application of edge tractions and lateral pressure alone are obtained the general axisymmetric problem is solved implicitly and the theory is applied to the solution of two representative examples existing small strain theories are shown to correspond to a singular limit of the general theory at which the underlying system changes from elliptic to parabolic type

how to deal with the unbounded in optimization theory and algorithms the aim of this survey is to show how the unbounded arises in optimization problems and how it leads to fundamental notions which are not only useful for proving theoretical results such as convergence of algorithms and the existence of optimal solutions but also for constructing new methods

on self concordant barrier functions for conic hulls and fractional programming given a self concordant barrier function for a convex set figure not available see fulltext we determine a self concordant barrier function for the conic hull figure not available see fulltext of figure not available see fulltext as our main result we derive an optimal barrier for figure not available see fulltext based on the barrier function for figure not available see fulltext important applications of this result include the conic reformulation of a convex problem and the solution of fractional programs by interior point methods the problem of minimizing a convex concave fraction over some convex set can be solved by applying an interior point method directly to the original nonconvex problem or by applying an interior point method to an equivalent convex reformulation of the original problem our main result allows to analyze the second approach showing that the rate of convergence is of the same order in both cases

a new computational framework for materials with different mechanical responses in tension and compression and its applications abstract materials possessing tension compression asymmetric behavior can be simulated by a bi modulus constitutive relation which assumes the materials have different moduli in tension and compression traditional iteration methods struggle for the convergence difficulty for such kind of constitutive model in this paper a new computational framework is established solution procedures under both small and finite deformations which have asymptotically quadratic rate of convergence have also been proposed and implemented in abaqus with umat numerical examples show that the proposed computational framework can be applied successfully to simulate the wrinkling analysis of thin plane membranes and explain some unusual cell mechanosensing phenomena