consistent tangent matrices for substepping schemes a very simple and general expression of the consistent tangent matrix for substepping time integration schemes is presented if needed the derivatives required for the computation of the consistent tangent moduli can be obtained via numerical differentiation these two strategies substepping and numerical differentiation lead to quadratic convergence in complex nonlinear inelasticity problems

a multiple imputation approach to cox regression with interval censored data we propose a general semiparametric method based on multiple imputation for cox regression with interval censored data the method consists of iterating the following two steps first from finite interval censored but not right censored data exact failure times are imputed using tanner and wei s poor man s or asymptotic normal data augmentation scheme based on the current estimates of the regression coefficient and the baseline survival curve second a standard statistical procedure for right censored data such as the cox partial likelihood method is applied to imputed data to update the estimates through simulation we demonstrate that the resulting estimate of the regression coefficient and its associated standard error provide a promising alternative to the nonparametric maximum likelihood estimate our proposal is easily implemented by taking advantage of existing computer programs for right censored data

effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

factorable fir nyquist filters with least stopband energy under sidelobe level constraints spectrally factorable nyquist filters are used in data communications to avoid intersymbol interference an approach is developed for obtaining a nyquist filter that is factorable having the smallest stopband energy for a given sidelobe level the resulting constrained minimization problem is solved efficiently and reliably using the goldfarb idnani 1983 algorithm some examples are presented comparing the present method with a previous approach from the literature

bivariate latent variable models for clustered discrete and continuous outcomes abstract we use the concept of a latent variable to derive the joint distribution of a continuous and a discrete outcome and then extend the model to allow for clustered data the model can be parameterized in a way that allows one to write the joint distribution as a product of a standard random effects model for the continuous variable and a correlated probit model for the discrete variable this factorization suggests a convenient approach to parameter estimation using quasi likelihood techniques our approach is motivated by the analysis of developmental toxicity experiments for which a number of discrete and continuous outcomes are measured on offspring clustered within litters fetal weight and malformation data illustrate the results

positive numerical integration methods for chemical kinetic systems abstract chemical kinetics conserves mass and renders nonnegative solutions a good numerical simulation would ideally produce mass balanced positive concentration vectors many time stepping methods are mass conservative however unconditional positivity restricts the order of a traditional method to one the projection method presented in this paper ensures mass conservation and positivity first a numerical approximation is computed with one step of a mass preserving traditional scheme if there are negative components the nearest vector in the reaction simplex is found by solving a quadratic optimization problem this vector is shown to better approximate the true solution a simpler version involves just one projection step and stabilizes the reaction simplex this technique works best when the underlying time stepping scheme favors positivity projected methods are more accurate than clipping and allow larger time steps for kinetic systems which are unstable outside the positive quadrant

universal anisotropic yield criterion based on superquadric functional representation part 1 algorithmic issues and accuracy analysis abstract a robust and efficient stress update algorithm for the anisotropic yield criterion represented in the form of superquadric function introduced by barlat et al is presented it relies on a discrete variational formulation of the lagrangian functional which results from the principle of maximum plastic dissipation numerical solution of the discretized equations of evolution is based on the operator split methodology and the newton raphson method a line search algorithm is implemented to overcome numerical instabilities and to expand the convergence region of the basic newton raphson solution procedure the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discrete kuhn tucker condition numerical testing of the integration algorithm based on iso error maps is provided for several variants of the yield function

constrained least squares design of 2 d fir filters we consider the design of 2 d linear phase finite impulse response fir filters according to the least squares ls error criterion subject to equality and or inequality constraints since we use a frequency domain formulation these constraints can be used to explicitly prescribe frequency dependent error tolerances the maximum minimum or fixed values of the frequency response at certain points and or regions our method combines lagrange multiplier and kuhn tucker theory to solve a much wider class of problems than do standard methods it allows arbitrary compromises between the ls and the equiripple design

optimal design of nonlinear phase fir filters with prescribed phase error constrained least squares design and constrained chebyshev design of one and two dimensional nonlinear phase fir filters with prescribed phase error are considered in this paper by a unified semi infinite positive definite quadratic programming approach in order to obtain unique optimal solutions we propose to impose constraints on the complex approximation error and the phase error by introducing a sigmoid phase error constraint bound function the group delay error can be greatly reduced a goldfarb idnani based algorithm is presented to solve the semi infinite positive definite quadratic program resulting from the constrained least squares design problem and then applied after some modifications to the constrained chebyshev design problem which is proved in this paper to be equivalent also to a semi infinite positive definite quadratic program through design examples the proposed method is compared with several existing methods simulation results demonstrate the effectiveness and efficiency of the proposed method

modeling survival data with informative cluster size analysis of clustered data focusing on inference of the marginal distribution may be problematic when the risk of the outcome is related to the cluster size termed as informative cluster size in the absence of censoring hoffman et al proposed a within cluster resampling method which is asymptotically equivalent to a weighted generalized estimating equations score equation we investigate the estimation of the marginal distribution for multivariate survival data with informative cluster size using cluster weighted weibull and cox proportional hazards models the cluster weighted cox model can be implemented using standard software simulation results demonstrate that the proposed methods produce unbiased parameter estimation in the presence of informative cluster size to illustrate the proposed approach we analyze survival data from a lymphatic filariasis study in recife brazil

computational complexity certification for real time mpc with input constraints based on the fast gradient method this paper proposes to use nesterov s fast gradient method for the solution of linear quadratic model predictive control mpc problems with input constraints the main focus is on the method s a priori computational complexity certification which consists of deriving lower iteration bounds such that a solution of pre specified suboptimality is obtained for any possible state of the system we investigate cold and warm starting strategies and provide an easily computable lower iteration bound for cold starting and an asymptotic characterization of the bounds for warm starting moreover we characterize the set of mpc problems for which small iteration bounds and thus short solution times are expected the theoretical findings and the practical relevance of the obtained lower iteration bounds are underpinned by various numerical examples and compared to certification results for a primal dual interior point method

an efficient implementation of an active set method for svms we propose an active set algorithm to solve the convex quadratic programming qp problem which is the core of the support vector machine svm training the underlying method is not new and is based on the extensive practice of the simplex method and its variants for convex quadratic problems however its application to large scale svm problems is new until recently the traditional active set methods were considered impractical for large svm problems by adapting the methods to the special structure of svm problems we were able to produce an efficient implementation we conduct an extensive study of the behavior of our method and its variations on svm problems we present computational results comparing our method with joachims svmlight see joachims 1999 the results show that our method has overall better performance on many svm problems it seems to have a particularly strong advantage on more difficult problems in addition this algorithm has better theoretical properties and it naturally extends to the incremental mode since the proposed method solves the standard svm formulation as does svmlight the generalization properties of these two approaches are identical and we do not discuss them in the paper

a sub stepping scheme for multi scale analysis of solids abstract this paper proposes a sub stepping procedure aimed at saving overall computing time in the finite element solution of non linear solid mechanics problems where homogenization based multi scale constitutive models are used to describe the material response the procedure obtains better initial guesses for the newton raphson scheme adopted in the solution of the incremental equilibrium problem of the representative volume element rve associated with each gauss quadrature point of the discretised macroscopic continuum the resulting gain in robustness of the rve newton raphson iteration allows larger time load steps to be prescribed at the macroscopic scale leading to substantial savings in computing time the proposed sub stepping preserves the quadratic rate of asymptotic convergence of the macroscopic scale newton raphson scheme without compromising the accuracy of the solution numerical examples demonstrate that the achieved improvement in efficiency is particularly noticeable under the assumption of finite stains where overall speed up factors of up to four are observed

a regularized decomposition method for minimizing a sum of polyhedral functions a problem of minimizing a sum of many convex piecewise linear functions is considered in view of applications to two stage linear programming where objectives are marginal values of lower level problems it is assumed that domains of objectives may be proper polyhedral subsets of the space of decision variables and are defined by piecewise linear induced feasibility constraints we propose a new decomposition method that may start from an arbitrary point and simultaneously processes objective and feasibility cuts for each component the master program is augmented with a quadratic regularizing term and comprises an a priori bounded number of cuts the method goes through nonbasic points in general and is finitely convergent without any nondegeneracy assumptions next we present a special technique for solving the regularized master problem that uses an active set strategy and qr factorization and exploits the structure of the master finally some numerical evidence is given

analysis of failure time data with dependent interval censoring summary this article develops a method for the analysis of screening data for which the chance of being screened is dependent on the event of interest informative censoring because not all subjects make all screening visits the data on the failure of interest is interval censored we propose a model that will properly adjust for the dependence to obtain an unbiased estimate of the nonparametric failure time function and we provide an extension for applying the method for estimation of the regression parameters from a discrete time proportional hazards regression model the method is applied on a data set from an observational study of cytomegalovirus shedding in a population of hiv infected subjects who participated in a trial conducted by the aids clinical trials group

a cholesky dual method for proximal piecewise linear programming a quadratic programming method is given for minimizing a sum of piecewise linear functions and a proximal quadratic term subject to simple bounds on variables it may be used for search direction finding in nondifferentiable optimization algorithms an efficient implementation is described that updates a cholesky factorization of active constraints and provides good accuracy via iterative refinement numerical experience is reported for some large problems

a joint model for survival and longitudinal data measured with error the relationship between a longitudinal covariate and a failure time process can be assessed using the cox proportional hazards regression model we consider the problem of estimating the parameters in the cox model when the longitudinal covariate is measured infrequently and with measurement error we assume a repeated measures random effects model for the covariate process estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process this approach uses the available information optimally because we use both the covariate and survival data simultaneously parameters are estimated using the expectation maximization algorithm we argue that such a method is superior to naive methods where one maximizes the partial likelihood of the cox model using the observed covariate values it also improves on two stage methods where in the first stage empirical bayes estimates of the covariate process are computed and then used as time dependent covariates in a second stage to find the parameters in the cox model that maximize the partial likelihood

numerical experience with lower bounds for miqp branch and bound the solution of convex mixed integer quadratic programming miqp problems with a general branch and bound framework is considered it is shown how lower bounds can be computed efficiently during the branch and bound process improved lower bounds such as the ones derived in this paper can reduce the number of quadratic programming qp problems that have to be solved the branch and bound approach is also shown to be superior to other approaches in solving miqp problems numerical experience is presented which supports these conclusions

marginal analyses of clustered data when cluster size is informative we propose a new approach to fitting marginal models to clustered data when cluster size is informative this approach uses a generalized estimating equation gee that is weighted inversely with the cluster size we show that our approach is asymptotically equivalent to within cluster resampling hoffman sen and weinberg 2001 biometrika 73 13 22 a computationally intensive approach in which replicate data sets containing a randomly selected observation from each cluster are analyzed and the resulting estimates averaged using simulated data and an example involving dental health we show the superior performance of our approach compared to unweighted gee the equivalence of our approach with wcr for large sample sizes and the superior performance of our approach compared with wcr when sample sizes are small

exact complexity certification of active set methods for quadratic programming active set methods are recognized to often outperform other methods in terms of speed and solution accuracy when solving small size quadratic programming qp problems making them very attractive in embedded linear model predictive control mpc applications a drawback of active set methods is the lack of tight bounds on the worst case number of iterations a fundamental requirement for their implementation in a real time system extensive simulation campaigns provide an indication of the expected worst case computation load but not a complete guarantee this paper solves such a certification problem by proposing an algorithm to compute the exact bound on the maximum number of iterations and floating point operations required by a state of the art dual active set qp solver the algorithm is applicable to a given qp problem whose linear term of the cost function and right hand side of the constraints depend linearly on a vector of parameters as in the case of linear mpc in addition a new solver is presented that combines explicit and implicit mpc ideas guaranteeing improvements of the worst case computation time the ability of the approach to exactly quantify memory and worst case computation requirements is tested on a few mpc examples also highlighting when online optimization should be preferred to explicit mpc

nonlinear multi scale homogenization with different structural models at different scales summary we present an extension of the computational homogenization theory to cases where different structural models are used at different scales and no energy potential can be defined at the small scale we observe that volumetric averaging which is not applicable in such cases unless similarities exist in the macro scale and micro scale models is not a necessary prerequisite to carry out computational homogenization at each material point of the macro model we replace the conventional representative volume element with a representative domain element rde to link the large scale and small scale problems we then introduce a linear operator mapping the smooth part of the small scale displacement field of each rde to the large scale strain field and a trace operator to impose boundary conditions in the rde the latter is defined on the basis of engineering judgement analogously to the conventional theory a generalized hill s condition rather than being invoked is derived from duality principles and is used to recover the stress measures at the large scale for the implementation in a nonlinear finite element analysis control nodes and constraint equations are used the effectiveness of the procedure is demonstrated for three beam to truss example problems for which multi scale convergence is numerically analysed copyright 2013 john wiley sons ltd

optimization based limiters for the spectral element method abstract we introduce a new family of optimization based limiters for the h p spectral element method the native spectral element advection operator is oscillatory but due to its mimetic properties it is locally conservative and has a monotone property with respect to element averages we exploit this property to construct locally conservative quasimonotone and sign preserving limiters the quasimonotone limiter prevents all overshoots and undershoots at the element level but is not strictly non oscillatory it also maintains quasimonotonicity even with the addition of a dissipation term such as viscosity or hyperviscosity the limiters are based on a least squares formulation with equality and inequality constraints and are local to each element we evaluate the new limiters using a deformational flow test case for advection on the surface of the sphere we focus on mesh refinement for moderate p 3 and high order p 6 elements as expected the spectral element method obtains its formal order of accuracy for smooth problems without limiters for advection of fields with cusps and discontinuities the high order convergence is lost but in all cases p 6 outperforms p 3 for the same degrees of freedom

regression analysis of clustered interval censored data with informative cluster size interval censored data are commonly found in studies of diseases that progress without symptoms which require clinical evaluation for detection several techniques have been suggested with independent assumption however the assumption will not be valid if observations come from clusters furthermore when the cluster size relates to response variables commonly used methods can bring biased results for example in a study on lymphatic filariasis a parasitic disease where worms make several nests in the infected person s lymphatic vessels and reside until adulthood the response variable of interest is the nest extinction times as the extinction times of nests are checked by repeated ultrasound examinations exact extinction times are not observed instead data are composed of two examination points the last examination time with living worms and the first examination time with dead worms furthermore as williamson et al statistics in medicine 2008 27 543 555 pointed out larger nests show a tendency for low clearance rates this association has been denoted as an informative cluster size to analyze the relationship between the numbers of nests and interval censored nest extinction times this study proposes a joint model for the relationship between cluster size and clustered interval censored failure data a proportional hazard model with random effect and a mixed ordinal regression model are applied to failure times and cluster size respectively the joint model approach addresses both the association among failure times from the same cluster and the dependency of failure times on cluster size simulation studies are performed to assess the finite sample properties of the estimators and lymphatic filariasis data are analyzed as an illustration

marginal analysis of correlated failure time data with informative cluster sizes we consider modeling correlated survival data when cluster sizes may be informative to the outcome of interest based on a within cluster resampling wcr approach and a weighted score function wsf method we derive the large sample properties for the wcr estimators under the cox proportional hazards model we establish consistency and asymptotic normality of the regression coefficient estimators and the weak convergence property of the estimated baseline cumulative hazard function the wsf method is to incorporate the inverse of cluster sizes as weights in the score function we conduct simulation studies to assess and compare the finite sample behaviors of the estimators and apply the proposed methods to a dental study as an illustration

two scale kinematics and linearization for simultaneous two scale analysis of periodic heterogeneous solids at finite strain abstract we introduce the notion of two scale kinematics and the procedure of two scale linearization which are indispensable to the simultaneous two scale analysis method for the mechanical behavior of periodic heterogeneous solids at finite strain these are accomplished by formulating the two scale boundary value problem in both material and spatial descriptions with reference to the two scale modeling strategy developed in comput methods appl mech engrg 190 40 41 2001 5427 that utilized the convergence results of mathematical homogenization the formulation brings the intimate relationship between micro and macro scale kinematics in describing the micro macro coupling behavior inherent in heterogeneous media it is also shown that the two scale linearization necessitates the strict consistency with the micro scale equilibrated state and naturally invites the tangential homogenization process for both material and spatial descriptions several numerical examples of simultaneous two scale computations are presented to illustrate the two scale nature of the deformation of a heterogeneous solid at finite strain

an ol n 3 primal interior point algorithm for convex quadratic programming we present a primal interior point method for convex quadratic programming which is based upon a logarithmic barrier function approach this approach generates a sequence of problems each of which is approximately solved by taking a single newton step it is shown that the method requires o sqrt n l iterations and o n3 5l arithmetic operations by using modified newton steps the number of arithmetic operations required by the algorithm can be reduced to o n3l

homogenization based multiscale crack modelling from micro diffusive damage to macro cracks the existence of a representative volume element rve for a class of quasi brittle materials having a random heterogeneous microstructure in tensile shear and mixed mode loading is demonstrated by deriving traction separation relations which are objective with respect to rve size a computational homogenization based multiscale crack modelling framework implemented in an fe2 setting for quasi brittle solids with complex random microstructure is presented the objectivity of the macroscopic response to the micro sample size is shown by numerical simulations therefore a homogenization scheme which is objective with respect to macroscopic discretization and microscopic sample size is devised numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed method

low rank modifications of riccati factorizations for model predictive control in model predictive control mpc the control input is computed by solving a constrained finite time optimal control cftoc problem at each sample in the control loop the main computational effort when solving the cftoc problem using an active set as method is often spent on computing the search directions which in mpc corresponds to solving unconstrained finite time optimal control uftoc problems this is commonly performed using riccati recursions or generic sparsity exploiting algorithms in this paper the focus is efficient search direction computations for as type methods the system of equations to be solved at each as iteration is changed only by a low rank modification of the previous one and exploiting this structured change is important for the performance of as type solvers in this paper theory for how to exploit these low rank changes by modifying the riccati factorization between as iterations in a structured way is presented a numerical evaluation of the proposed algorithm shows that the computation time can be significantly reduced by modifying instead of re computing the riccati factorization this speedup can be important for as type solvers used for linear nonlinear and hybrid mpc

time discretized variational formulation of non smooth frictional contact the present work extends the non smooth contact class of algorithms introduced by kane et al to the case of friction the formulation specifically addresses contact geometries e g involving multiple collisions between tightly packed non smooth bodies for which neither normals nor gap functions can be properly defined a key aspect of the approach is that the incremental displacements follow from a minimum principle the objective function comprises terms which account for inertia strain energy contact friction and external forcing the euler lagrange equations corresponding to this extended variational principle are shown to be consistent with the equations of motion of solids in frictional contact in addition to its value as a basis for formulating numerical algorithms the variational framework offers theoretical advantages as regards the selection of trajectories in cases of non uniqueness we present numerical and analytical examples which demonstrate the good momentum and energy conservation characteristics of the numerical algorithms as well as the ability of the approach to account for stick and slip conditions

analysis of clustered and interval censored data from a community based study in asthma many authors in recent years have proposed extensions of familiar survival analysis methodologies to apply in dependent data settings for example when data are clustered or subject to repeated measures however these extensions have been considered largely in the context of right censored data in this paper we discuss a parametric frailty model for the analysis of clustered and interval censored failure time data details are presented for the specific case where the underlying time to event data follow a weibull distribution maximum likelihood estimates will be obtained using commercially available software and the empirical efficiency of these estimators will be explored via a simulation study we also discuss a score test to make inferences about the magnitude and significance of over dispersion in clustered data settings these methods will be illustrated using data from the east boston asthma study

computational micro to macro transitions for discretized micro structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy the paper investigates algorithms for the computation of homogenized stresses and overall tangent moduli of micro structures undergoing large strain deformations typically these micro structures define representative volumes of nonlinear heterogeneous materials such as inelastic composites polycrystalline aggregates or particle assemblies we consider a priori given discretized micro structures without focussing on details of specific discretization techniques for space and time the key contribution of the paper is the construction of a family of algorithms and matrix representations of overall properties of discretized micro structures which are motivated by a minimization of averaged incremental energy it is shown that the overall stresses and tangent moduli of a typical micro structure may exclusively be defined in terms of discrete forces and stiffness properties on the boundary we focus on deformation driven micro structures where the overall macroscopic deformation is controlled in this context three classical types of boundary conditions are investigated i linear deformation ii uniform tractions and iii periodic deformation and antiperiodic tractions incorporated by lagrangian multiplier methods these conditions generate three classes of constrained minimization problems with associated solution algorithms for the computation of equilibrium states and overall properties of micro structures the proposed algorithms and matrix representations of the overall properties are formally independent of the interior spatial structure and the local constitutive response of the micro structure and are therefore applicable to a broad class of model problems we demonstrate their performance for some representative model problems including finite elastic plastic deformations of composites texture developments in polycrystalline materials and equilibrium states of particle assemblies

updating conjugate directions by the brgs formula many iterative algorithms for optimization calculations form positive definite second derivative approximations b say automatically butb is not stored explicitly because of the need to solve equations of the formbd g we consider working with matricesz whose columns satisfy the conjugacy conditionsz 1 bz 1 particular attention is given to updatingz in a way that corresponds to revisingb by the bfgs formula a procedure is proposed that seems to be much more stable than the direct use of a product formula 1 an extension to this procedure provides some automatic rescaling of the columns ofz which avoids some inefficiencies due to a poor choice of the initial second derivative approximation our work is also relevant to active set methods for linear inequality constraints to updating the cholesky factorization ofb and to explaining some properties of the bfgs algorithm

structural damage identification using piezoelectric sensors in this paper a two stage damage identification method has been proposed using the data obtained from piezoelectric sensors in the first stage a first order approximation technique is presented for numerically predicting the transient response of electrical potential change on sensors caused by damages both numerical and experimental data in the time domain are transformed into the frequency domain using the fft technique the damage locations can then be detected by matching the numerical data and the experimental data in the frequency domain through a proposed detection technique after identifying the possible damage locations in the second stage an iterative estimation scheme for solving nonlinear optimization programming problems based on the quadratic programming technique is put forward to predict damage extents a beam example has been employed to illustrate the effectiveness of the algorithm numerically furthermore various investigations such as the accuracy of the proposed first order approximation technique the influences of the excitation frequency of external force and modelling errors and measurement noises on the results have been carried out

an example of cycling in a feasible point algorithm an example shows that if in rosen s 4 algorithm for calculating a point that satisfies linear constraints a natural criterion is used to select constraints to delete from active sets then the algorithm may cycle instead of converging there are no degeneracies in the example

a nonlinear programming heuristic for computing optimal link capacities in a multi hour alternate routing communications network we consider the problem of determining the optimal number of communications channels in a telecommunications network traffic between pairs of nodes is assumed to vary with the time of day traffic between two nodes can flow over a one link direct path or if no direct channels are available over a two link alternate route the problem is to compute the optimal number of channels on each link to minimize cost subject to a constraint that enough trunks are present so that the probability of no idle channel does not exceed a specified amount the mathematical formulation of this problem known as the multi hour engineering problem yields an integer nonlinear programming problem nlp we apply recursive quadratic programming with exact penalty function epf line searches to solve the continuous nlp and use the special problem structure to provide a starting point and epf parameter a simple heuristic is used to obtain integral number of channels satisfying desired blocking objectives the method successfully solved a set of randomly generated test problems with up to 35 variables and 432 nonlinear constraints

interval regression analysis by quadratic programming approach when we use linear programming in possibilistic regression analysis some coefficients tend to become crisp because of the characteristic of linear programming on the other hand a quadratic programming approach gives more diverse spread coefficients than a linear programming one therefore to overcome the crisp characteristic of linear programming we propose interval regression analysis based on a quadratic programming approach another advantage of adopting a quadratic programming approach is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression by changing the weights of the quadratic function we can analyze the given data from different viewpoints for data with crisp inputs and interval outputs the possibility and necessity models can be considered therefore the unified quadratic programming approach obtaining the possibility and necessity regression models simultaneously is proposed even though there always exist possibility estimation models the existence of necessity estimation models is not guaranteed if we fail to assume a proper function fitting to the given data as a regression model thus we consider polynomials as regression models since any curve can be represented by the polynomial approximation using polynomials we discuss how to obtain approximation models which fit well to the given data where the measure of fitness is newly defined to gauge the similarity between the possibility and the necessity models furthermore from the obtained possibility and necessity regression models a trapezoidal fuzzy output can be constructed

an adaptive sub incremental strategy for the solution of homogenization based multi scale problems abstract in this contribution several schemes for the solution of homogenization based multi scale constitutive problems undergoing finite strains with inelastic material behavior are investigated these schemes are aimed at improving the robustness and efficiency of the newton raphson method in the multilevel finite element ml fem framework an adaptive sub incremental strategy is proposed for the discrete representative volume element rve boundary value problem the procedure is able to ensure the convergence of the solution algorithm in the presence of several sources of non linearity and obtains improved initial guesses for the newton raphson scheme in the ml fem framework the enlargement of the convergence bowl of the newton raphson procedure at the micro scale allows larger macroscopic deformation gradients to be prescribed and significantly reduces the overall computational cost of ml fem analyses the proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the newton raphson scheme at the macroscopic level numerical examples of both micro scale and two scale finite element simulations are presented to demonstrate the improved robustness and efficiency of the solution procedures proposed

a null space method for computing the search direction in the general inertia controlling method for dense quadratic programming the inertia controlling strategy in active set methods consists of choosing the working set so that the reduced hessian never has more than one non positive eigenvalue usually this strategy has been implemented by permitting to delete constraints only at stationary points in a general inertia controlling method constraints may be deleted at non stationary points a null space method for dense quadratic programming is presented in which only one triangular system has to be solved at each iteration for computing the search direction this method takes advantage of previously developed recurrence formulas for updating the search direction when the working set changes

active set algorithm for mathematical programs with linear complementarity constraints in the paper an incomplete active set algorithm is given for mathematical programs with linear complementarity constraints mplcc at each iteration a finite number of inner iterations are contained for approximately solving the relaxed nonlinear optimization problem if the feasible region of the mplcc is bounded under the uniform linear independence constraint qualification licq any cluster point of the sequence generated from the algorithm is a b stationary point of the mplcc preliminary numerical tests show that the algorithm is promising

piecewise linear approximations in nonconvex nonsmooth optimization we present a bundle type method for minimizing nonconvex nondifferentiable functions of several variables the algorithm is based on the construction of both a lower and an upper polyhedral approximation of the objective function in particular at each iteration a search direction is computed by solving a quadratic program aiming at maximizing the difference between the lower and the upper model a proximal approach is used to guarantee convergence to a stationary point under the hypothesis of weak semismoothness

signs of divided differences yield least squares data fitting with constrained monotonicity or convexity methods are presented for least squares data smoothing by using the signs of divided differences of the smoothed values professor m j d powell initiated the subject in the early 1980s and since then theory algorithms and fortran software make it applicable to several disciplines in various ways let us consider n data measurements of a univariate function which have been altered by random errors then it is usual for the divided differences of the measurements to show sign alterations which are probably due to data errors we make the least sum of squares change to the measurements by requiring the sequence of divided differences of order m to have at most q sign changes for some prescribed integer q the positions of the sign changes are integer variables of the optimization calculation which implies a combinatorial problem whose solution can require about o nq quadratic programming calculations in n variables and n m constraints suitable methods have been developed for the following cases it has been found that a dynamic programming procedure can calculate the global minimum for the important cases of piecewise monotonicity m 1 q 1 and piecewise convexity concavity m 2 q 1 of the smoothed values the complexity of the procedure in the case of m 1 is o n2 qn log2 n computer operations while it is reduced to only o n when q 0 monotonicity and q 1 increasing decreasing monotonicity the case m 2 q 1 requires o qn2 computer operations and n2 quadratic programming calculations which is reduced to one and n 2 quadratic programming calculations when m 2 q 0 i e convexity and m 2 q 1 i e convexity concavity respectively unfortunately the technique that receives this efficiency cannot generalize for the highly nonlinear case m 3 q 2 however the case m 3 q 0 is solved by a special strictly convex quadratic programming calculation and the case m 3 q 1 can be solved by at most 2 n m applications of the previous algorithm also as m gets larger large sets of active constraints usually occur at the optimal approximation which makes the calculation for higher values of q less expensive than what it seems to further attention is given to the sensitivity of the solution with respect to changes in the constraints and the data the smoothing technique is an active research topic and there seems to be room for further developments one strong reason for studying methods that make use of divided differences for data smoothing is that whereas only the data are provided the achieved accuracy goes much beyond the accuracy of the data at an order determined automatically by the chosen divided differences

an incremental method for solving convex finite min max problems we introduce a new approach to minimizing a function defined as the pointwise maximum over finitely many convex real functions next referred to as the component functions with the aim of working on the basis of incomplete knowledge of the objective function a descent algorithm is proposed which need not require at the current point the evaluation of the actual value of the objective function namely of all the component functions thus extending to min max problems the philosophy of the incremental approaches widely adopted in the nonlinear least squares literature given the nonsmooth nature of the problem we resort to the well established machinery of bundle methods we provide global convergence analysis of our method and in addition we study a subgradient aggregation scheme aimed at simplifying the problem of finding a tentative step this paper is completed by the numerical results obtained on a set of standard test problems

minimizing nonconvex nonsmooth functions via cutting planes and proximity control we describe an extension of the classical cutting plane algorithm to tackle the unconstrained minimization of a nonconvex not necessarily differentiable function of several variables the method is based on the construction of both a lower and an upper polyhedral approximation to the objective function and is related to the use of the concept of proximal trajectory convergence to a stationary point is proved for weakly semismooth functions

a numerically stable dual method for solving strictly convex quadratic programs an efficient and numerically stable dual algorithm for positive definite quadratic programming is described which takes advantage of the fact that the unconstrained minimum of the objective function can be used as a starting point its implementation utilizes the cholesky and qr factorizations and procedures for updating them the performance of the dual algorithm is compared against that of primal algorithms when used to solve randomly generated test problems and quadratic programs generated in the course of solving nonlinear programming problems by a successive quadratic programming code the principal motivation for the development of the algorithm these computational results indicate that the dual algorithm is superior to primal algorithms when a primal feasible point is not readily available the algorithm is also compared theoretically to the modified simplex type dual methods of lemke and van de panne and whinston and it is illustrated by a numerical example

a weighted gram schmidt method for convex quadratic programming range space methods for convex quadratic programming improve in efficiency as the number of constraints active at the solution decreases in this paper we describe a range space method based upon updating a weighted gram schmidt factorization of the constraints in the active set the updating methods described are applicable to both primal and dual quadratic programming algorithms that use an active set strategy

damage assessment of structures using modal test data abstract system health monitoring of structures is important not only for conducting safe operation but also maintaining system performance in this paper two identification algorithms for assessing structural damages using the modal test data have been developed an important characteristic in the present approaches is that the employment of the global numerical models e g fem model and some important information e g young s modulus of structures are avoided to a great extent as the first step of the damage identification two algorithms for the detection of damage location are proposed which are similar in concept to the subspace rotation algorithm or best achievable eigenvector technique furthermore a quadratic programming model is set up for the two approaches to predict the damage extent to demonstrate the capability of the proposed approaches an example of a 10 bay planar truss structure is employed for checking the present approaches numerically furthermore the experimental data from the vibration test of a beam with two fixed ends are used directly in the present approaches the final results show that the present techniques perform quite well in spite of the little structural information and measurement inaccuracies

on the superlinear convergence of a trust region algorithm for nonsmooth optimization it is proved that the second order correction trust region algorithm of fletcher 5 ensures superlinear convergence if some mild conditions are satisfied

reconstructing convex sets from support line measurements algorithms are proposed for reconstructing convex sets given noisy support line measurements it is observed that a set of measured support lines may not be consistent with any set in the plane a theory of consistent support lines which serves as a basis for reconstruction algorithms that take the form of constrained optimization algorithms is developed the formal statement of the problem and constraints reveals a rich geometry that makes it possible to include prior information about object position and boundary smoothness the algorithms which use explicit noise models and prior knowledge are based on maximum likelihood and maximum a posteriori estimation principles and are implemented using efficient linear and quadratic programming codes experimental results are presented this research sets the stage for a more general approach to the incorporation of prior information concerning the estimation of object shape

primal and dual active set methods for convex quadratic programming computational methods are proposed for solving a convex quadratic program qp active set methods are defined for a particular primal and dual formulation of a qp with general equality constraints and simple lower bounds on the variables in the first part of the paper two methods are proposed one primal and one dual these methods generate a sequence of iterates that are feasible with respect to the equality constraints associated with the optimality conditions of the primal dual form the primal method maintains feasibility of the primal inequalities while driving the infeasibilities of the dual inequalities to zero the dual method maintains feasibility of the dual inequalities while moving to satisfy the primal inequalities in each of these methods the search directions satisfy a kkt system of equations formed from hessian and constraint components associated with an appropriate column basis the composition of the basis is specified by an active set strategy that guarantees the nonsingularity of each set of kkt equations each of the proposed methods is a conventional active set method in the sense that an initial primal or dual feasible point is required in the second part of the paper it is shown how the quadratic program may be solved as a coupled pair of primal and dual quadratic programs created from the original by simultaneously shifting the simple bound constraints and adding a penalty term to the objective function any conventional column basis may be made optimal for such a primal dual pair of shifted penalized problems the shifts are then updated using the solution of either the primal or the dual shifted problem an obvious application of this approach is to solve a shifted dual qp to define an initial feasible point for the primal or vice versa the computational performance of each of the proposed methods is evaluated on a set of convex problems from the cutest test collection

numerical homogenization of periodic composite materials with non linear material components in this paper a numerically developed homogenized constitutive relation for the global behaviour of periodic composite materials with elasto plastic components is derived the algorithm presented is general and can be applied to any kind of non linear material behaviour respecting the complementarity rule the method different from those presented in the literature is currently restricted to small strains plane problems and monotonic proportional loading conditions copyright 1999 john wiley sons ltd

on a class of constitutive equations in viscoplasticity formulation and computational issues the viscoplastic constitutive model is formulated based on the existence of the dissipation potential which embodies the notion of the gauge minkowski function of the convex set a perturbation method is used for a solution of stiff differential equations characterizing the associated problem of evolution it relies on a discrete formulation of viscoplasticity which results from the regularized version of the principle of maximum plastic dissipation the operator split methodology and the newton raphson method are used to obtain the numerical solution of the discretized equations of evolution the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discretized evolution equations for several variants of the flow potential function including some representative stiff functional forms numerical tests of the integration algorithm based on iso error maps are provided finally a numerical example is presented to illustrate the robustness and the effectiveness of the proposed approach

a global piecewise smooth newton method for fast large scale model predictive control in this paper the strictly convex quadratic program qp arising in model predictive control mpc for constrained linear systems is reformulated as a system of piecewise affine equations a regularized piecewise smooth newton method with exact line search on a convex differentiable piecewise quadratic merit function is proposed for the solution of the reformulated problem the algorithm has considerable merits when applied to mpc over standard active set or interior point algorithms its performance is tested and compared against state of the art qp solvers on a series of benchmark problems the proposed algorithm is orders of magnitudes faster especially for large scale problems and long horizons for example for the challenging crude distillation unit model of pannocchia rawlings and wright 2007 with 252 states 32 inputs and 90 outputs the average running time of the proposed approach is 1 57 ms

coupling traffic models on networks and urban dispersion models for simulating sustainable mobility strategies the aim of the present paper is to investigate the viability of macroscopic traffic models for modeling and testing different traffic scenarios in order to define the impact on air quality of different strategies for the reduction of traffic emissions to this aim we complement a well assessed traffic model on networks garavello and piccoli 2006 1 with a strategy for estimating data needed from the model and we couple it with the urban dispersion model sirane soulhac 2000 2

marginal regression models for multivariate failure time data abstract in this article we propose a general cox type regression model to formulate the marginal distributions of multivariate failure time data this model has a nested structure in that it allows different baseline hazard functions among distinct failure types and imposes a common baseline hazard function on the failure times of the same type we prove that the maximum quasi partial likelihood estimator for the vector of regression parameters under the independence working assumption is consistent and asymptotically normal with a covariance matrix for which a consistent estimator is provided furthermore we establish the uniform consistency and joint weak convergence of the aalen breslow type estimators for the cumulative baseline hazard functions and develop a resampling technique to approximate the joint distribution of these processes which enables one to make simultaneous inference about the survival functions over the time axis and across failure types finally we assess the small sample pro

application of sequential quadratic programming software program to an actual problem we produced a nonlinear optimization software program which is based on a sequential quadratic programming sqp method schittkowski 1981a our program has several original characteristics 1 automatic choice between two qp solvers the goldfarb idnani gi method goldfarb and idnani 1983 and the least squares ls method schittkowski 1981b 2 an augmented lagrange function schittkowski 1981a as the objective function for line search 3 adaptive armijo method for line search 4 direct definition of upper and lower bounds for variables and constraint functions and 5 accurate numerical differentials these characteristics ensure the reliability of our program for solving standard problems in this paper point 3 is described in detail then the program is applied to an actual problem the optimal placement of blocks a model for this problem has been suggested by sha and dutton 1984 but it was unsuited to treatment by the sqp method thus we modify it to ensure program applicability

within cluster resampling within cluster resampling is proposed as a new method for analysing clustered data although the focus of this paper is clustered binary data the within cluster resampling asymptotic theory is general for many types of clustered data within cluster resampling is a simple but computationally intensive estimation method its main advantage over other marginal analysis methods such as generalised estimating equations liang zeger 1986 zeger liang 1986 is that it remains valid when the risk for the outcome of interest is related to the cluster size which we term nonignorable cluster size we present theory for the asymptotic normality and provide a consistent variance estimator for the within cluster resampling estimator simulations and an example are developed that assess the finite sample behaviour of the new method and show that when both methods are valid its performance is similar to that of generalised estimating equations

semiparametric regression analysis of interval censored data summary we propose a semiparametric approach to the proportional hazards regression analysis of interval censored data an em algorithm based on an approximate likelihood leads to an m step that involves maximizing a standard cox partial likelihood to estimate regression coefficients and then using the breslow estimator for the unknown baseline hazards the e step takes a particularly simple form because all incomplete data appear as linear terms in the complete data log likelihood the algorithm of turnbull 1976 journal of the royal statistical society series b38 290 295 is used to determine times at which the hazard can take positive mass we found multiple imputation to yield an easily computed variance estimate that appears to be more reliable than asymptotic methods with small to moderately sized data sets in the right censored survival setting the approach reduces to the standard cox proportional hazards analysis while the algorithm reduces to the one suggested by clayton and cuzick 1985 applied statistics34 148 156 the method is illustrated on data from the breast cancer cosmetics trial previously analyzed by finkelstein 1986 biometrics42 845 854 and several subsequent authors