a preconditioner for the steady state navier stokes equations we present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady state navier stokes equations also known as the oseen equations the solver is an iterative method of krylov subspace type for which we devise a preconditioner through a heuristic argument based on the fundamental solution tensor for the oseen operator the preconditioner may also be conceived through a weaker heuristic argument involving differential operators computations indicate that convergence for the preconditioned discrete oseen problem is only mildly dependent on the viscosity inverse reynolds number and most importantly that the number of iterations does not grow as the mesh size is reduced indeed since the preconditioner is motivated through analysis of continuous operators the number of iterations decreases for smaller mesh size which accords with better approximation of these operators

a general class of shift splitting preconditioners for non hermitian saddle point problems with applications to time harmonic eddy current models abstract based on a general splitting of the 1 1 leading block matrix we first construct a general class of shift splitting gcss preconditioners for non hermitian saddle point problems convergence conditions of the corresponding matrix splitting iteration methods and preconditioning properties of the gcss preconditioned saddle point matrices are analyzed then the gcss preconditioner is specifically applied to the non hermitian saddle point problems arising from the finite element discretizations of the hybrid formulations of the time harmonic eddy current models with suitable choices of the splittings the new gcss preconditioners are easier to implement and have faster convergence rates than the existing shift splitting preconditioner and its modified variant two numerical examples are presented to verify the theoretical results and show effectiveness of the new proposed preconditioners

constrained least square design of fir filters without specified transition bands this paper puts forth the notion that explicitly specified transition bands have been introduced in the filter design literature in part as an indirect approach for dealing with discontinuities in the desired frequency response we suggest that the use of explicitly specified transition bands is sometimes inappropriate because to satisfy a meaningful optimality criterion their use implicitly assumes a possibly unrealistic assumption on the class of input signals this paper also presents an algorithm for the design of peak constrained lowpass fir filters according to an integral square error criterion that does not require the use of specified transition bands this rapidly converging robust simple multiple exchange algorithm uses lagrange multipliers and the kuhn tucker conditions on each iteration the algorithm will design linear and minimum phase fir filters and gives the best l sub 2 filter and a continuum of chebyshev filters as special cases it is distinct from many other filter design methods because it does not exclude from the integral square error a region around the cut off frequency and yet it overcomes the gibbs phenomenon without resorting to windowing or smoothing out the discontinuity of the ideal lowpass filter

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

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

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

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

optimization algorithms for the solution of the frictionless normal contact between rough surfaces this paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half plane using the boundary element method bem after recasting the resulting linear complementarity problem lcp as a convex quadratic program qp with nonnegative constraints different optimization algorithms are compared for its solution i a greedy method based on different solvers for the unconstrained linear system conjugate gradient cg gauss seidel cholesky factorization ii a constrained cg algorithm iii the alternating direction method of multipliers admm and iv the non negative least squares nnls algorithm possibly warm started by accelerated gradient projection steps or taking advantage of a loading history the latter method is two orders of magnitude faster than the greedy cg method and one order of magnitude faster than the constrained cg algorithm finally we propose another type of warm start based on a refined criterion for the identification of the initial trial contact domain that can be used in conjunction with all the previous optimization algorithms this method called cascade multi resolution cmr takes advantage of physical considerations regarding the scaling of the contact predictions by changing the surface resolution the method is very efficient and accurate when applied to real or numerically generated rough surfaces provided that their power spectral density function is of power law type as in case of self affine fractal surfaces

parameterized approximate block lu preconditioners for generalized saddle point problems abstract in this paper we are concerned with the iteration solution of generalized saddle point problems based on the exact block lu factorization of the coefficient matrix we construct a class of parameterized approximate block lu factorization preconditioners which rely on suitable approximations of the schur complement of the 1 1 block of the coefficient matrix convergence of the corresponding iteration methods is analyzed and the optimal iteration parameters minimizing the spectral radii are deduced algebraic characteristics of the related preconditioned matrices are discussed including eigenvalue and eigenvector distributions and upper bounds for degree of the minimal polynomial the established results extend those of the approximate factorization and variants of the hermitian and skew hermitian splitting and positive and skew hermitian splitting preconditioners for saddle point problems numerical experiments are demonstrated to illustrate the efficiency of the new preconditioners

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

variational inference of the fiber orientation density using diffusion mr imaging diffusion mr imaging has enabled the in vivo exploration of the connectional architecture in human brain this method particularly reveals the complex system of long range nerve fibers that integrate the functionally distinct areas of the cerebral cortex since the fibers are not directly observed but the diffusion process of water molecules in the underlying material a forward model is established that maps the microgeometry of nervous tissue onto the diffusion weighted signals this article proposes the spherical deconvolution of the fiber orientation density in a reproducing kernel hilbert space thereby generalizing previous approaches that perform a truncated fourier analysis on the sphere the specified inverse problem is solved within a smoothing spline framework which preserves the characteristic properties of a density function namely its normalization and non negativity a gaussian process model allows the specification of confidence bands for the estimated fiber orientation density and the rigorous selection of the hyperparameters here the high frequency content in the density function and the noise variance of the mr observations in addition we weaken the constant diffusivity assumption frequently made in the spherical convolution methodology the novel approach which uncovers the fiber orientation field of white matter is demonstrated with diffusion weighted data sets featuring high angular resolution

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

an augmented lagrangian based approach to the oseen problem we describe an effective solver for the discrete oseen problem based on an augmented lagrangian formulation of the corresponding saddle point system the proposed method is a block triangular preconditioner used with a krylov subspace iteration like bicgstab the crucial ingredient is a novel multigrid approach for the 1 1 block which extends a technique introduced by schoberl for elasticity problems to nonsymmetric problems our analysis indicates that this approach results in fast convergence independent of the mesh size and largely insensitive to the viscosity we present experimental evidence for both isop2 p0 and isop2 p1 finite elements in support of our conclusions we also show results of a comparison with two state of the art preconditioners showing the competitiveness of our approach

a relaxed dimensional factorization preconditioner for the incompressible navier stokes equations in this paper we introduce a relaxed dimensional factorization rdf preconditioner for saddle point problems properties of the preconditioned matrix are analyzed and compared with those of the closely related dimensional splitting ds preconditioner recently introduced by benzi and guo 7 numerical results for a variety of finite element discretizations of both steady and unsteady incompressible flow problems indicate very good behavior of the rdf preconditioner with respect to both mesh size and viscosity

field of values convergence analysis of augmented lagrangian preconditioners for the linearized navier stokes problem we study a block triangular preconditioner for finite element approximations of the linearized navier stokes equations the preconditioner is based on the augmented lagrangian formulation of the problem and was introduced by the authors in siam j sci comput 28 2006 pp 2095 2113 in this paper we prove field of values type estimates for the preconditioned system which lead to optimal convergence bounds for the gmres algorithm applied to solve the system two variants of the preconditioner are considered an ideal one based on exact solves for the velocity submatrix and a more practical variant based on block triangular approximations of the velocity submatrix

a new optimal window signal processing an optimal window that can provide the best tradeoff between the peak sidelobe level and the total sidelobe level is presented necessary and sufficient conditions are established for the optimal window a design algorithm is presented and examples are discussed the examples demonstrate that the window is capable of much better performance than previously available windows such as the hamming window relationships between the maximum error and the mean squared error are explored for the window optimization problem it is concluded that the minimax and least squares approximations are both fundamentally inefficient this conclusion is supported by experimental evidence and mathematical analyses

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

semi nonparametric estimation of the call option price surface under strike and time to expiry no arbitrage constraints abstract we suggest a semi nonparametric estimator for the call option price surface the estimator is a bivariate tensor product b spline to enforce no arbitrage constraints across strikes and expiry dates we establish sufficient no arbitrage conditions on the control net of the b spline surface the conditions are linear and therefore allow for an implementation of the estimator by means of standard quadratic programming techniques the consistency of the estimator is proved by means of simulations we explore the statistical efficiency benefits that are associated with estimating option price surfaces and state price densities under the full set of no arbitrage constraints we estimate a call option price surface families of first order strike derivatives and state price densities for s p 500 option data

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

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

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

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

efficient preconditioning of the linearized navier stokes equations for incompressible flow we outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of navier stokes equations we describe a very general strategy for preconditioning that has two basic building blocks a multigrid v cycle for the scalar convection diffusion operator and a multigrid v cycle for a pressure poisson operator we present numerical experiments illustrating that a simple implementation of our approach leads to an effective and robust solver strategy in that the convergence rate is independent of the grid robust with respect to the time step and only deteriorates very slowly as the reynolds number is increased

block preconditioners based on approximate commutators this paper introduces a strategy for automatically generating a block preconditioner for solving the incompressible navier stokes equations we consider the pressure convection diffusion preconditioners proposed by kay loghin and wathen siam j sci comput 24 2002 pp 237 256 and silvester elman kay and wathen j comput appl math 128 2001 pp 261 279 numerous theoretical and numerical studies have demonstrated mesh independent convergence on several problems and the overall efficacy of this methodology a drawback however is that it requires the construction of a convection diffusion operator denoted f p projected onto the discrete pressure space this means that integration of this idea into a code that models incompressible flow requires a sophisticated understanding of the discretization and other implementation issues something often held only by the developers of the model as an alternative we consider automatic ways of computing f p based on purely algebraic considerations the new methods are closely related to the bfbt preconditioner of elman siam j sci comput 20 1999 pp 1299 1316 we use the fact that the preconditioner is derived from considerations of commutativity between the gradient and convection diffusion operators together with methods for computing sparse approximate inverses to generate the required matrix f p automatically we demonstrate that with this strategy the favorable convergence properties of the preconditioning methodology are retained

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

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

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

dynamic contact impact problems energy conservation and planetary gear trains abstract the paper is a continuation of the work presented in comp meth appl mech eng 190 2001 1903 aimed at modeling of a general class of dynamic contact impact problems for systems of rigid bodies the contact is assumed to be frictionless and the main challenge is to model the exchange between the kinetic and elastic energies in the system this calls for a discretization scheme that conserves linear and angular momentum and first of all the total energy at the discrete level such a scheme has been presented in comp meth appl mech eng 190 2001 1903 and in this work we complement it with a very general treatment of the no penetration condition for two elastic bodies the approach is based on the concept of the sign rvachev function and it provides a natural generalization of the classical point to line condition arch computat meth eng 2 1995 1 the work has been motivated with the modeling of planetary gear trains and has resulted in the first to our best knowledge two dimensional parallel finite element simulator for gear sets parallel finite element simulator of planetary gear trains ph d dissertation the university of texas 2001

finite element shakedown analysis of two dimensional structures in the present paper the formulation proposed by casciaro and garcea comput meth appl mech eng 2002 191 5761 5792 and applied to the shakedown analysis of plane frames is extended to the analysis of two dimensional flat structures in both the cases of plane stress and plane strain the discrete formulation is obtained using a mixed finite element in which both stress and displacement fields are interpolated the material is assumed to be elasto plastic and a linearization of the elastic domain is performed the result is a versatile iterative scheme well suited to implementation in general purpose fem codes an extensive series of numerical tests is presented showing the reliability of the proposed formulation copyright 2005 john wiley sons ltd

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

a case study in exploratory functional data analysis geometrical features of the internal carotid artery this pilot study is a product of the aneurisk project a scientific program that aims at evaluating the role of vascular geometry and hemodynamics in the pathogenesis of cerebral aneurysms by means of functional data analyses we explore the aneurisk dataset to highlight the relations between the geometric features of the internal carotid artery expressed by its radius profile and centerline curvature and the aneurysm location after introducing a new similarity index for functional data we eliminate ancillary variability of vessel radius and curvature profiles through an iterative registration procedure we then reduce data dimension by means of functional principal components analysis last a quadratic discriminant analysis of functional principal components scores allows us to discriminate patients with aneurysms in different districts

least squares preconditioners for stabilized discretizations of the navier stokes equations this paper introduces two stabilization schemes for the least squares commutator lsc preconditioner developed by elman howle shadid shuttleworth and tuminaro siam j sci comput 27 2006 pp 1651 1668 for the incompressible navier stokes equations this preconditioning methodology is one of several choices that are effective for navier stokes equations and it has the advantage of being defined from strictly algebraic considerations it has previously been limited in its applicability to div stable discretizations of the navier stokes equations this paper shows how to extend the same methodology to stabilized low order mixed finite element approximation methods

parameter optimization using the l exact penalty function and strictly convex quadratic programming problems abstract this paper presents an algorithm for the numerical solution of constrained parameter optimization problems the solution strategy is based on a sequential quadratic programming sqp technique that uses the l exact penalty function unlike similar sqp algorithms the method proposed here solves only strictly convex quadratic programs to obtain the search directions the global convergence properties of the algorithm are enhanced by the use of a nonmonotone line search and second order corrections to avoid the maratos effect the paper also presents an ansi c implementation of the algorithm the effectiveness of the proposed method is demonstrated by solving numerous parameter optimization and optimal control problems that have appeared in the literature

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

a class of rank two ellipsoid algorithms for convex programming in this paper we develop a method for constructing minimum volume ellipsoids containing a wedge shaped subset of a given ellipsoid this construction yields a class of ellipsoid algorithms for convex programming that use rank two update formulae

analysis of augmented lagrangian based preconditioners for the steady incompressible navier stokes equations we analyze a class of modified augmented lagrangian based preconditioners for both stable and stabilized finite element discretizations of the steady incompressible navier stokes equations we study the eigenvalues of the preconditioned matrices obtained from picard linearization and we devise a simple and effective method for the choice of the augmentation parameter gamma based on fourier analysis numerical experiments on a wide range of model problems demonstrate the robustness of these preconditioners yielding fast convergence independent of mesh size and only mildly dependent on viscosity on both uniform and stretched grids good results are also obtained on linear systems arising from newton linearization we also show that performing inexact preconditioner solves with an algebraic multigrid algorithm results in excellent scalability comparisons of the modified augmented lagrangian preconditioners with other state of the art techniques show the competitiveness of our approach

two modified block triangular splitting preconditioners for generalized saddle point problems abstract for the generalized saddle point problems firstly we introduce a modified generalized relaxed splitting mgrs preconditioner to accelerate the convergence rate of the krylov subspace methods based on a block triangular splitting of the saddle point matrix secondly we propose a modified block triangular splitting mbts this new preconditioner is easily implemented since it has simple block structure the spectral properties and the degrees of the minimal polynomials of the preconditioned matrices are discussed respectively moreover we apply the mgrs and the mbts preconditioners to three dimensional linearized navier stokes equations then we derive the quasi optimal parameters of the mgrs and the mbts preconditioners for two and three dimensional navier stokes equations respectively finally numerical experiments are illustrated to show the preconditioning effects of the two new preconditioners

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

stability and preconditioning for a hybrid approximation on the sphere this paper proposes a new preconditioning scheme for a linear system with a saddle point structure arising from a hybrid approximation scheme on the sphere an approximation scheme that combines local spherical radial basis functions and global spherical polynomials in principle the resulting linear system can be preconditioned by the block diagonal preconditioner of murphy golub and wathen making use of a recently derived inf sup condition and the brezzi stability and convergence theorem for this approximation scheme we show that in this context the schur complement in the above preconditioner is spectrally equivalent to a certain non constant diagonal matrix numerical experiments with a non uniform distribution of data points support the theoretically proved quality of the new preconditioner

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

a variant of relaxed triangular splitting preconditioners for generalized saddle point problems from navier stokes equations abstract based on the dimensional split preconditioner in this paper a variant of relaxed triangular splitting preconditioner vrts is presented and discussed in which a simple and feasible way is designed for the selection of the parameters spectral properties of the vrts preconditioned matrix are analyzed in detail theoretical analysis shows that when applying the vrts preconditioner within a krylov subspace method less computational cost is required at each iteration than some state of the art approaches finally some numerical experiments arising from the discretization of navier stokes equations are given to illustrate and validate the efficiency and robustness of the presented preconditioners with using gmres as an iterative solver

on choices of iteration parameter in hss method the hss iteration method is effective to solve non hermitian positive definite linear systems but the choice of its optimal parameter is a difficult and challenging problem in theoretical analysis and practical computations in this paper we obtain an accurate estimate to the optimal parameter of the hss iteration method by adopting a reasonable and simple optimization principle numerical experiments show that this principle is feasible to produce an accurate estimate to the optimal parameter of the hss iteration method

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

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

application of theorem of minimum potential energy to a complex structure part i two dimensional analysis a cylindrical shell with a non circular cross section consisting of flat sides and circular arc corners is analyzed using the theorem of minimum potential energy the three dimensional analysis builds on previous two dimensional work the potential energy expression for the structure is developed including first order transverse shear deformation effects all unknown displacements are represented by power series and the potential energy expression is rewritten in terms of the summation convention for the power series the variation of the potential energy expression is taken leading to a linear system of equations that is solved for the unknown power series coefficients with the displacements determined stresses are calculated for a composite sandwich construction an examination of both short shells less than twice the boundary layer length and long shells more than twice the boundary layer length is made the mpe method with power series is found to predict behavior well for short shells but not for long shells

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

parameter estimates for the relaxed dimensional factorization preconditioner and application to hemodynamics we present new results on the relaxed dimensional factorization rdf preconditioner for solving saddle point problems from incompressible flow simulations first introduced in benzi et al 2011 this method contains a parameter 0 0 to be chosen by the user previous works provided an estimate of in the 2d case using local fourier analysis a novel algebraic estimation technique for finding a suitable value of the rdf parameter in both the 2d and the 3d case with arbitrary geometries is proposed this technique is tested on a variety of discrete saddle point problems arising from the approximation of the navier stokes equations using a marker and cell scheme and a finite element one we also show results for a large scale problem relevant for hemodynamics simulation that we solve in parallel using up to 8196 cores

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

optimal nonnegative definite approximations of estimated moving average covariance sequences the problem of finding the closest nonnegative definite moving average covariance sequence to a given estimate which may not be nonnegative definite is considered an algorithm is developed which is based on a set of constrained minimization problems each parameterized by the zero frequencies of the spectral density function corresponding to the optimal solution the algorithm entails first solving a simple minimization problem with linear constraints whose closed form solution is given by a projection onto a subspace these solutions lie either outside the set of nonnegative definite sequences or on its boundary if the solution lies on the boundary it is the optimal solution the problem is considered directly in the space of covariance sequence elements as a result the nonlinear maximization step is performed on sets of low dimension by considering the minimization problem in this space it is possible to characterize some of the geometrical properties of the optimal solution in terms of the locations of its zero frequencies

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

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

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